Academic Journal
S-preclones and the Galois connection S Pol– S Inv, Part I
| العنوان: | S-preclones and the Galois connection S Pol– S Inv, Part I |
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| المؤلفون: | Jipsen, Peter, Lehtonen, Erkko, Pöschel, Reinhard |
| المصدر: | Mathematics, Physics, and Computer Science Faculty Articles and Research |
| بيانات النشر: | Chapman University Digital Commons |
| سنة النشر: | 2024 |
| المجموعة: | Chapman University Digital Commons |
| مصطلحات موضوعية: | Partially ordered algebra, Preclone, Galois connection, Orderpreserving map, Order-reversing map, Algebra |
| الوصف: | We consider S-operations f : An → A in which each argument is assigned a signum s ∈ S representing a “property†such as being order- preserving or order-reversing with respect to a fixed partial order on A. The set S of such properties is assumed to have a monoid structure reflecting the behaviour of these properties under the composition of S-operations (e.g., order-reversing composed with order-reversing is order- preserving). The collection of all S-operations with prescribed properties for their signed arguments is not a clone (since it is not closed under arbitrary identification of arguments), but it is a preclone with special properties, which leads to the notion of S-preclone. We introduce S-relations = (s)s∈S, S-relational clones, and a preservation property (f S), and we consider the induced Galois connection SPol–SInv. The S-preclones and S-relational clones turn out to be exactly the closed sets of this Galois connection. We also establish some basic facts about the structure of the lattice of all S-preclones on A. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | unknown |
| Relation: | https://digitalcommons.chapman.edu/scs_articles/1044; https://digitalcommons.chapman.edu/context/scs_articles/article/2043/viewcontent/S_preclones_and_the_Galois_connection_SPol_SInv_Part_I.pdf |
| DOI: | 10.1007/s00012-024-00863-7 |
| الاتاحة: | https://digitalcommons.chapman.edu/scs_articles/1044 https://doi.org/10.1007/s00012-024-00863-7 https://digitalcommons.chapman.edu/context/scs_articles/article/2043/viewcontent/S_preclones_and_the_Galois_connection_SPol_SInv_Part_I.pdf |
| Rights: | The authors ; http://creativecommons.org/licenses/by/4.0/ |
| رقم الانضمام: | edsbas.E6A572BB |
| قاعدة البيانات: | BASE |
| DOI: | 10.1007/s00012-024-00863-7 |
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