Academic Journal
On intervals and isometries of $MV$-algebras
| العنوان: | On intervals and isometries of $MV$-algebras |
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| المؤلفون: | Jakubík, Ján |
| بيانات النشر: | Institute of Mathematics, Academy of Sciences of the Czech Republic Matematický ústav AV ČR |
| سنة النشر: | 2002 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | keyword:$MV$-algebra, keyword:duality, keyword:interval, keyword:autometrization, keyword:2-periodic isometry, msc:06D35 |
| الوصف: | summary:Let Int $\mathcal A$ be the lattice of all intervals of an $MV$-algebra $\mathcal A$. In the present paper we investigate the relations between direct product decompositions of $\mathcal A$ and (i) the lattice Int $\mathcal A$, or (ii) 2-periodic isometries on $\mathcal A$, respectively. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0011-4642 1572-9141 |
| Relation: | mr:MR1923269; zbl:Zbl 1012.06013; reference:[1] G. Birkhoff: Lattice Theory.AMS Colloquium Publications. Vol. XXV, Providence, RI, 1967. Zbl 0153.02501, MR 0227053; reference:[2] G. Cattaneo and F. Lombardo: Independent axiomatization of $MV$-algebras.Tatra Mt. Math. Publ. 15 (1998), 227–232. MR 1655091; reference:[3] C. C. Chang: Algebraic analysis of many valued logics.Trans. Amer. Math. Soc. 88 (1958), 467–490. Zbl 0084.00704, MR 0094302, 10.1090/S0002-9947-1958-0094302-9; reference:[4] P. Conrad: Lattice Ordered Groups.Tulane University, New Orleans, 1970. Zbl 0258.06011; reference:[5] D. Glushankof: Cyclic ordered groups and $MV$-algebras.Czechoslovak Math. J. 44(119) (1994), 725–739.; reference:[6] Ch. Holland: Intrinsic metrics for lattice ordered groups.Algebra Universalis 19 (1984), 142–150. Zbl 0557.06011, MR 0758313, 10.1007/BF01190425; reference:[7] J. Jakubík: Isometries of lattice ordered groups.Czechoslovak Math. J. 30(105) (1980), 142–152. MR 0565917; reference:[8] J. Jakubík: Direct product decompositions of $MV$-algebras.Czechoslovak Math. J. 44(119) (1994), 725–739. MR 1295146; reference:[9] J. Jakubík and M. Kolibiar: On some properties of pairs of lattices.Czechoslovak Math. J. 4(79) (1954), 1–27. (Russian) MR 0065529; reference:[10] M. Jasem: Weak isometries and direct decompositions of dually residuated lattice ordered semigroups.Math. Slovaca 43 (1993), 119–136. Zbl 0782.06012, MR 1274597; reference:[11] J. Lihová: Posets having a selfdual interval poset.Czechoslovak Math. J. 44(119) (1994), 523–533. MR 1288170; reference:[12] P. Mangani: On certain algebras related to many-valued logics.Boll. Un. Mat. Ital. 8 (1973), 68–78. (Italian); reference:[13] D. Mundici: Interpretation of $AFC^*$-algebras in Łukasiewicz sentential calculus.J. Funct. Anal. 65 (1986), 15–63. MR 0819173, 10.1016/0022-1236(86)90015-7; reference:[14] W. B. Powell: On isometries in abelian lattice ordered groups.J. Indian Math. Soc. 46 (1982), 189–194. MR 0878072; reference:[15] J. Rachůnek: Isometries in ordered groups.Czechoslovak Math. J. 34(109) (1984), 334–341. MR 0743498; reference:[16] K. L. Swamy: Isometries in autometrized lattice ordered groups.Algebra Universalis 8 (1977), 58–64. Zbl 0457.06015, MR 0463074; reference:[17] K. L. Swamy: Isometries in autometrized lattice ordered groups II.Math. Seminar Notes, Kobe Univ. 5 (1977), 211–214. Zbl 0457.06015, MR 0463075 |
| الاتاحة: | http://hdl.handle.net/10338.dmlcz/127751 |
| Rights: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use |
| رقم الانضمام: | edsbas.CA3BF59F |
| قاعدة البيانات: | BASE |
Full Text Finder | تدمد: | 00114642 15729141 |
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