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1Academic Journal
المؤلفون: Száz, Árpád
مصطلحات موضوعية: keyword:vector spaces, keyword:linear and affine subspaces, keyword:linear relations, msc:15A03, msc:15A04, msc:26E25, msc:46A22, msc:47A06
وصف الملف: application/pdf
Relation: mr:MR2026171; zbl:Zbl 1104.26305; reference:[1] Adasch N.: Der Satz über offene lineare Relationen in topologischen Vektorräumen.Note Mat. 11 (1991), 1-5. MR 1258535; reference:[2] Arens R.: Operational calculus of linear relations.Pacific J. Math. 11 (1961), 9-23. Zbl 0102.10201, MR 0123188, 10.2140/pjm.1961.11.9; reference:[3] Berge C.: Topological Spaces Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity.Oliver and Boyd London (1963). Zbl 0114.38602, MR 1464690; reference:[4] Cross R.: Multivalued Linear Operators.Marcel Dekker New York (1998). Zbl 0911.47002, MR 1631548; reference:[5] Dacić R.: On multi-valued functions.Publ. Inst. Math. (Beograd) (N.S.) 9 (1969), 5-7. MR 0257991; reference:[6] Findlay G.D.: Reflexive homomorphic relations.Canad. Math. Bull. 3 (1960), 131-132. Zbl 0100.28002, MR 0124251, 10.4153/CMB-1960-015-x; reference:[7] Godini G.: Set-valued Cauchy functional equation.Rev. Roumaine Math. Pures Appl. 20 (1975), 1113-1121. Zbl 0322.39013, MR 0393920; reference:[8] Holá L'.: Some properties of almost continuous linear relations.Acta Math. Univ. Comenian. 50-51 (1987), 61-69. MR 0989404; reference:[9] Holá L'., Kupka I.: Closed graph and open mapping theorems for linear relations.Acta Math. Univ. Comenian. 46-47 (1985), 157-162. MR 0872338; reference:[10] Holá L'., Maličký P.: Continuous linear selectors of linear relations.Acta Math. Univ. Comenian. 48-49 (1986), 153-157. MR 0885328; reference:[11] Kelley J.L., Namioka I.: Linear Topological Spaces.D. Van Nostrand New York (1963). Zbl 0115.09902, MR 0166578; reference:[12] Nikodem K.: K-convex and K-concave set-valued functions.Zeszty Nauk. Politech. Lódz. Mat. 559 (1989), 1-75.; reference:[13] Robinson S.M.: Normed convex processes.Trans. Amer. Math. Soc. 174 (1972), 127-140. MR 0313769, 10.1090/S0002-9947-1972-0313769-9; reference:[14] Smajdor W.: Subadditive and subquadratic set-valued functions.Prace Nauk. Univ. Ślask. Katowic. 889 (1987), 1-73. Zbl 0626.54019, MR 0883802; reference:[15] Száz Á.: Pointwise limits of nets of multilinear maps.Acta Sci. Math. (Szeged) 55 (1991), 103-117. MR 1124949; reference:[16] Száz Á.: The intersection convolution of relations and the Hahn-Banach type theorems.Ann. Polon. Math. 69 (1998), 235-249. MR 1665007, 10.4064/ap-69-3-235-249; reference:[17] Száz Á.: An extension of Kelley's closed relation theorem to relator spaces.Filomat (Nis) 14 (2000), 49-71. Zbl 1012.54026, MR 1953994; reference:[18] Száz Á.: Preseminorm generating relations and their Minkowski functionals.Publ. Elektrotehn. Fak. Univ. Beograd, Ser. Mat. 12 (2001), 16-34. Zbl 1060.46004, MR 1920353; reference:[19] Száz Á.: Translation relations, the building blocks of compatible relators.Math. Montisnigri, to appear. MR 2023739; reference:[20] Száz Á., Száz G.: Additive relations.Publ. Math. Debrecen 20 (1973), 259-272. MR 0340878; reference:[21] Száz Á., Száz G.: Linear relations.Publ. Math. Debrecen 27 (1980), 219-227. MR 0603995; reference:[22] Ursescu C.: Multifunctions with convex closed graph.Czechoslovak Math. J. 25 (1975), 438-441. Zbl 0318.46006, MR 0388032; reference:[23] Wilhelm M.: Criteria of openness of relations.Fund. Math. 114 (1981), 219-228. MR 0644407, 10.4064/fm-114-3-219-228
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2Academic Journal
المؤلفون: Baronti, Marco, Fragnelli, Vito, Lewicki, Grzegorz
مصطلحات موضوعية: keyword:linear operator, keyword:extension of minimal norm, keyword:element of best approximation, keyword:strongly unique best approximation, msc:41A35, msc:41A52, msc:41A55, msc:41A65, msc:46A22, msc:47A20
وصف الملف: application/pdf
Relation: mr:MR1364484; zbl:Zbl 0831.41014; reference:[1] Baronti M., Papini P.L.: Norm one projections onto subspaces of $l^p$.Ann. Mat. Pura Appl. IV (1988), 53-61. MR 0980971; reference:[2] Blatter J., Cheney E.W.: Minimal projections onto hyperplanes in sequence spaces.Ann. Mat. Pura Appl. 101 (1974), 215-227. MR 0358179; reference:[3] Collins H.S., Ruess W.: Weak compactness in spaces of compact operators and vector valued functions.Pacific J. Math. 106 (1983), 45-71. MR 0694671; reference:[4] Odyniec Wl., Lewicki G.: Minimal Projections in Banach Spaces.Lecture Notes in Math. 1449, Springer-Verlag. Zbl 1062.46500, MR 1079547; reference:[5] Singer I.: On the extension of continuous linear functionals.Math. Ann. 159 (1965), 344-355. Zbl 0141.12002, MR 0188758; reference:[6] Singer I.: Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces.Springer-Verlag, Berlin, Heidelberg, New York, 1970. Zbl 0197.38601, MR 0270044; reference:[7] Sudolski J., Wojcik A.: Some remarks on strong uniqueness of best approximation.Approximation Theory and its Applications 6 (1990), 44-78. Zbl 0704.41016, MR 1078687
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3Academic Journal
المؤلفون: Kakol, Jerzy
مصطلحات موضوعية: keyword:Hahn-Banach extension property, keyword:topological vector space, msc:46A22
وصف الملف: application/pdf
Relation: mr:MR1240183; zbl:Zbl 0777.46003; reference:[1] Duren P.L., Romberg R.C., Shields A.L.: Linear functionals in $H^p$-spaces with $0; reference:[2] Kalton N.J.: Basic sequences in $F$-spaces and their applications.Proc. Edinburgh Math. Soc. 19 (1974), 151-167. Zbl 0296.46010, MR 0415259; reference:[3] Kakol J.: Nonlocally convex spaces and the Hahn-Banach extension property.Bull. Acad. Polon. Sci. 33 (1985), 381-393. Zbl 0588.46004, MR 0821575; reference:[4] Klee V.: Exotic topologies for linear spaces.Proc. Symposium on General Topology and its Relations to Modern Algebra, Prague, 1961. Zbl 0111.10701, MR 0154088; reference:[5] Shapiro J.H.: Examples of proper closed weakly dense subspaces in non-locally convex $F$-spaces.Israel J. Math. 7 (1969), 369-380. Zbl 0202.39303, MR 0257696; reference:[6] Wilansky A.: Topics in Functional Analysis.Springer Verlag 45 (1967). Zbl 0156.36103, MR 0223854
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4Academic Journal
المؤلفون: Thierfelder, Jörg
وصف الملف: application/pdf
Relation: mr:MR1150940; zbl:Zbl 0778.46005; reference:[1] W. Bonnice, R. Silverman: The Hahn-Banach extension and the least upper bound properties are equivalent.Proc. Amer. Math. Soc. 18 (1967), 843 - 850. Zbl 0165.46802, MR 0215050; reference:[2] J. M. Borwein: Continuity and differentiability properties of convex operators.Proc. London Math. Soc. 44 (1982), 3, 420-444. Zbl 0487.46026, MR 0656244; reference:[3] J. M. Borwein: On the Hahn-Banach extension property.Proc. Amer. Math. Soc. 86 (1982), 1,42-46. Zbl 0499.46002, MR 0663863; reference:[4] K.-H. Elster, J. Thierfelder: A general concept on cone approximations in nondifferentiable optimization.In: Nondifferentiable Optimization: Motivations and Applications (V. F. Demjanov; D. Pallaschke, eds.).(Lecture Notes in Economics and Mathematical Systems vol. 255.) Springer-Verlag, Berlin-Heidelberg-New York-Tokyo 1985, pp. 170-189. MR 0822014; reference:[5] R. B. Holmes: Geometric Functional Analysis and its Applications.Springer-Verlag, Berlin-Heidelberg-New York 1975. Zbl 0336.46001, MR 0410335; reference:[7] G. Jameson: Ordered Linear Spaces.(Lecture Notes in Mathematics, vol. 141.) Springer- Verlag, Berlin -Heidelberg-New York 1970. Zbl 0196.13401, MR 0438077; reference:[8] G. Köthe: Topologische Lineare Raume I.Springer-Verlag, Berlin-Heidelberg-New York 1966. MR 0194863; reference:[9] R. Nehse: The Hahn-Banach property and equivalent conditions.Comment. Math. Univ. Carolinae 19 (1978), 1, 165-177. Zbl 0373.46011, MR 0492379; reference:[10] R. Nehse: Separation of two sets in product spaces.Math. Nachrichten 97 (1980), 179-187. MR 0600832; reference:[11] R. Nehse: Zwei Fortsetzungssätze.Wiss. Zeitschrift TH Ilmenau 30 (1984), 49-57. Zbl 0566.46002, MR 0749750; reference:[12] A. L. Peressini: Ordered Topological Vector Spaces.Harper and Row, New York-Evanston-London 1967. Zbl 0169.14801, MR 0227731; reference:[13] J. Thierfelder: Nonvertical affine manifolds and separation theorems in product spaces (to appear). MR 1121215; reference:[14] T. O. To: The equivalence of the least upper bound property and the Hahn-Banach property in ordered linear spaces.Proc. Amer. Math. Soc. 30 (1971), 287-295. MR 0417746; reference:[15] M. Valadier: Sous-differentiabilité des fonctions convexes a valeurs dans un espace vectoriel ordoné.Math. Scand. 30 (1972), 65-74. MR 0346525; reference:[16] J. Zowe: Subdifferential of convex functions with values in ordered vector spaces.Math. Scand. 34(1974), 69-83. MR 0380400
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5Academic Journal
المؤلفون: Kąkol, Jerzy, Sorjonen, Pekka
مصطلحات موضوعية: keyword:locally convex space, keyword:orthogonality space, keyword:Hahn--Banach extension property, msc:46A03, msc:46A15, msc:46A16, msc:46A22, msc:46C99
وصف الملف: application/pdf
Relation: mr:MR1118287; zbl:Zbl 0749.46002; reference:[1] Kąkol J.: Basic sequences and non locally convex topological vector spaces.Rend. Circ. Mat. Palermo (2) 36 (1987), 95-102. MR 0944650; reference:[2] Kalton N.J., Peck N.T., Roberts J.W.: An F-space sampler.vol. 89 of London Mathematical Society Lecture Note Series, Cambridge University Press, 1984. Zbl 0556.46002, MR 0808777; reference:[3] Piziak R.: Mackey closure operators.J. London Math. Soc. 4 (1971), 33-38. Zbl 0253.06001, MR 0295977; reference:[4] Piziak R.: Sesquilinear forms in infinite dimensions.Pacific J. Math. 43 (2) (1972), 475-481. Zbl 0237.46007, MR 0318850; reference:[5] Sorjonen P.: Lattice-theoretical characterizations of inner product spaces.Studia Sci. Math. Hungarica 19 (1984), 141-149. Zbl 0588.46019, MR 0787796; reference:[6] Sorjonen P.: Hahn-Banach extension properties in linear orthogonality spaces.Funct. Approximatio, Comment. Math., to appear. Zbl 0793.46007, MR 1201711; reference:[7] Wilbur W.J.: Quantum logic and the locally convex spaces.Trans. Amer. Math. Soc. 207 (1975), 343-360. Zbl 0289.46019, MR 0367607
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6Conference
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7Conference
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8Academic Journal
المؤلفون: Vonkomerová, Marta
وصف الملف: application/pdf
Relation: mr:MR621916; zbl:Zbl 0457.46004; reference:[1] BIRKHOFF G.: Lattice theoгy.Зrd ed. Providence 1967.; reference:[2] FREMLIN D. H.: A direct proof of the Mathes-Wright integral extension theorem.J. London Math. soc., 11, 1975, 276-284. MR 0380345; reference:[3] FUTÁŠ E.: Extension of continuous functionals.Mat. Čas. 21, 1971, 191-198. MR 0303250; reference:[4] POTOCKÝ R.: On random variables having values in a vector lattice.Math. Slov., 27, 1977, 267-276. Zbl 0372.28012, MR 0536144; reference:[5] RIEČAN B.: On the lattice group valued measures.Čas. pro pěst. mat., 101, 1976, 343-349. MR 0499072; reference:[6] PИEЧAH Б.: O пpoдoлжeнии oпepaтopoв c знaчeниaми в линeйниx пoлyупopядoчeнныx пpocтpaнcтвax.Čas. pro pěst. mat., 93, 1968, 459-471. MR 0248544; reference:[7] VOLAUF P.: Extension and regulaгity of l-group valued measures.Math. Slovaca, 27, 1977, 47-53. MR 0476989; reference:[8] VOLAUF P.: Some questions of the theoгy of probability in ordered spaces.Kand. diz. práca, Bratislava 1977.; reference:[9] VOLAUF P.: On extension of maps with values in ordeгed space.Math. Slov. (to appear).; reference:[10] BУЛИX Б. 3.: Bвeдeниe в тeopию пoлyyпopядoчeнныx пpocтpaнcтв.Mocквa 1961.; reference:[11] WRIGHT J. D. M.: The measure extension pгoblem foг vector lattices.Annales de l'Institut Fourier (Grenoble), 21, 1971, 65-85. MR 0330411
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9Academic Journal
المؤلفون: Neumann, Michael
وصف الملف: application/pdf
Relation: mr:MR731989; zbl:Zbl 0525.46027; reference:[1] Ford L. R., Fulkerson D. R.: Flows in Networks.Princeton, New Jersey. Princeton University Press 1962. Zbl 0106.34802, MR 0159700; reference:[2] Fuchssteiner В.: An Abstract Disintegration Theorem.Pacific J. Math. 94, 303-309 (1981). Zbl 0491.28011, MR 0628582, 10.2140/pjm.1981.94.303; reference:[3] König H., Neumann M.: Mathepiatische Wirtschaftstheorie.Vorlesungsaiisarbeitung. Saarbrücken 1976.; reference:[4] Mazur S., Orlicz W.: Sur les espaces métriques linéaires II.Studia Math. 13, 137-179 (1953). Zbl 0052.11103, MR 0068730, 10.4064/sm-13-2-137-179; reference:[5] Peressini A. L.: Ordered Topological Vector Spaces.New York-Evanston-London. Harper and Row 1967. Zbl 0169.14801, MR 0227731; reference:[6] Pták V.: On a Theorem of Mazur and Orlicz.Studia Math. 75, 365-366 (1956). MR 0080880, 10.4064/sm-15-3-365-366; reference:[7] Vogel W.: Lineares Optimieren.Leipzig. Akad. Verlagsgesellschaft Geest & Portig 1970. Zbl 0197.45601, MR 0323337
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10Academic Journal
المؤلفون: Nowak, Marian
وصف الملف: application/pdf
Relation: mr:MR1014127; zbl:Zbl 0679.46022; reference:[1] Aliprantis C. D., Burkinshaw O.: Locally solid Riesz spaces.Academic Press, New York, 1978. Zbl 0402.46005, MR 0493242; reference:[2] Bourbaki N.: Espaces vectoriels topologiques.Ermanne et Cie, Paris, 1955. Zbl 0067.08302; reference:[3] Edwards R. E.: Functional analysis.Holt, Rinchart and Winston, New York, 1965. Zbl 0182.16101, MR 0221256; reference:[4] Hudzik H., Musielak J., Urbański R.: Linear operations in modular spaces.Comment. Math. 23 (1983), 33-40. MR 0709168; reference:[5] Kantorovich L. V., Akilov G. P.: Functional analysis.Nauka, Moscow, 1984. Zbl 0555.46001, MR 0788496; reference:[6] Köthe G.: Topological vector spaces. II.Springer-Verlag, New York, Heidelberg, Berlin, 1979. MR 0551623; reference:[7] Krasnoselskii M. A., Rutickii Ya. B.: Convex functions and Orlicz spaces.Noordhof Ltd. Groningen, 1961. MR 0126722; reference:[8] Luxemburg W. A.: Banach function spaces.Delft, 1955. Zbl 0068.09204, MR 0072440; reference:[9] Musielak J., Orlicz W.: Some remarks on modular spaces.Bull. Acad. Polon. Sci. 7 (1959), 661-668. Zbl 0099.09202, MR 0112017; reference:[10] Musielak J., Waszak A.: Linear continuous functional over some two-modular spaces.Colloquia Math. Soc. Janos Bolyai, 35, Functions, Series, Operators, Budapest 1980, 877-890. MR 0751051; reference:[11] Nakano H.: Modular semi-ordered linear spaces.Maruzen CO. Nihonbashi, Tokyo, 1951. MR 0038565; reference:[12] Nowak M.: On the finest of all linear topologies on Orlicz spaces for which $\varphi $-modular convergence implies convergence in these topologies. III.Bull. Pol. Ac. Math. 34 (1986), 19-26. MR 0850309; reference:[13] Nowak M.: A characterization of the Mackey topology $\tau{(L^{\varphi},L^{varphi^\ast})} on Orlicz spaces.ibidem 34 (1986), 577-583. MR 0884205; reference:[14] Nowak M.: Orlicz lattices with modular topology I.CMUC 30 (1989) 261-270. Zbl 0679.46021, MR 1014127; reference:[15] Nowak M.: On the order structure of Orlicz lattices.Bull. Pol. Ac. Math (to appear). Zbl 0767.46005, MR 1101668; reference:[16] Nowak M.: Mixed topology on normed function spaces. I.ibidem, (to appear). Zbl 0756.46005; reference:[17] Orlicz W.: A note on modular spaces. VII.Bull. Acad. Polon. Sci. 12 (1964), 305-309. Zbl 0135.16202, MR 0169032; reference:[18] Peressini A.: Order topological vector spaces.Harper and Row, New York, Evanston, London, 1967. MR 0227731; reference:[19] Waelbroeck L.: Topological vector spaces and algebras.Springer, Lect. Notes in Math. 230 (1971). Zbl 0225.46001, MR 0467234; reference:[20] Webb J. H.: Sequential convergence in locally convex spaces.Proc. Camb. Phil. Soc. 64 (1968), 341-364. Zbl 0157.20202, MR 0222602; reference:[21] Wnuk W.: Representations of Orlicz lattices.Dissert. Math. 235 (1984). Zbl 0566.46018, MR 0820077
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11Academic Journal
المؤلفون: Jokl, Luděk
مصطلحات موضوعية: msc:46A15, msc:46A22, msc:46A55, msc:46G05, msc:47H99, msc:52A07, msc:58C20, msc:90C25, msc:90C33, msc:90C48
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Relation: mr:MR647027; zbl:Zbl 0487.46002; reference:[1] R. T. ROCKAFELLAR: Convex analysis.Princeton University Press, 1970. Zbl 0193.18401, MR 0274683; reference:[2] A. D. IOFFE V. M. TICHOMIROV: Teorija ekstremalnych zadač.Nauka, Moskva, 1974.; reference:[3] V. BARBU, Th. PRECUPANU: Convexity and optimization in Banach spaces.Editura Academiei, Bucuresti-Sijthoof & Noordhoff Int. Publ. b.v., Alpen san de Rijn, 1978. MR 0513634
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12Academic Journal
المؤلفون: Nehse, Reinhard
وصف الملف: application/pdf
Relation: mr:MR609945; zbl:Zbl 0518.46005; reference:[1] HILDEBRANDT R.: Trennung von Mengen mittels konvexer Funktionen.Diplomarbeit, TH Ilmenau 1980.; reference:[2] HILDEBRANDT R., NEHSE B.: Separation by convex functionals.Conf. on Math. Programming, Eisenach 1980, Abstracts (to appear).; reference:[3] HOLMES R. B.: Geometric Functional Analysis and its Applications.Springer-Verlag, New York - Heidelberg - Berlin 1975. Zbl 0336.46001, MR 0410335; reference:[4] KANTOROWITSCH L. W., AKILOV G. P.: Functional. Analysis.Nauka, Moscow 1977 (in Russian). MR 0511615; reference:[5] KÖTHE G.: Topologische lineare Räume I.Springer-Verlag, Berlin - Heidelberg - New York 1966. MR 0194863; reference:[6] NEHSE R.: Problems in connection with the Hahn-Banach-Theorem.Proc. of the Summer-school "Nonlinear Analysis", Berlin 1979, Akad. Verlag (to appear). MR 0639925
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13Academic Journal
المؤلفون: Pták, Pavel
وصف الملف: application/pdf
Relation: mr:MR526150; zbl:Zbl 0387.46002; reference:[BG] R. BARTLE L. GRAVES: Mappings between function spaces.Trans. Amer. Math. Soc. 72 (1952), 400-413. MR 0047910; reference:[F] Z. PROLÍK: Three technical tools in uniform spaces.Seminar Uniform Spaces 1973-74 (directed by Z. Frolík), Math. Inst. of Czech. Academy of Sciences 1975, Prague, pp. 3-26. MR 0440510; reference:[I] J. ISBELL: Uniform Spaces.Amer. Math. Soc. 1964. Zbl 0124.15601; reference:[L] J. LINDENSTRAUSS: On nonlinear projections in Banach spaces.Mich. J. Math. 11 (1964), 263-287. Zbl 0195.42803, MR 0167821; reference:[Lu] D. J. LUTZER: Continuous extenders for pseudometrics.Seminar Uniform Spaces 1976-77 (directed by Z. Frolík), Math. Inst. of Czech. Academy of Sciences 1977, Prague, pp. 43-50.; reference:[V] G. VIDOSSICH: A theorem on uniformly continuous extensions of mappings defined in finite-dimensianal spaces.Israel J. Math. 7 (1969). MR 0250276; reference:[Vi] J. VILÍMOVSKÝ: Several classes of uniform spaces connected with Banach-valued mappings.Seminar Uniform Spaces 1976-77 (directed by Z. Frolík), Math. Inst. of Czech. Academy of Sciences 1978, Prague, pp. 83-100. MR 0431102; reference:[Z] M. ZAHRADNÍK: $l_1$-continuous partition of unity on normed spaces.Czech. Math. Journal 26 (101) (1976). MR 0410682
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14Academic Journal
المؤلفون: Charvát, František
وصف الملف: application/pdf
Relation: mr:MR0298391; zbl:Zbl 0232.47013; reference:[1] KANTOROWICZ, AKILOFF: Funcional analysis in normed sparces.(Russian), Moscow 1959.; reference:[2] SUCHOMLINOFF: On extension of linear functionals in complex and quaternion spaces.(Russian), Mat. Sb. 1938, 353-358.; reference:[3] NACHBIN: A theorem of Hahn-Banach type for linear transformation.TAMS 68 (1950), 28-46. MR 0032932; reference:[4] CHARVÁT: K problematice rozšiřování lineáních operací na modulech.Čas. pěst. matematiky (93) (1968), 371-377. MR 0254556
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