Congruence Extensions in Congruence–Modular Varieties
We investigate from an algebraic and topological point of view the minimal prime spectrum of a universal algebra, considering the prime congruences with respect to the term condition commutator. Then we use the topological structure of the minimal prime spectrum to study extensions of universal alge...
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MDPI AG
2024-11-01
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| Online Access: | https://www.mdpi.com/2075-1680/13/12/824 |
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| author | George Georgescu Leonard Kwuida Claudia Mureşan |
| author_facet | George Georgescu Leonard Kwuida Claudia Mureşan |
| author_sort | George Georgescu |
| collection | DOAJ |
| description | We investigate from an algebraic and topological point of view the minimal prime spectrum of a universal algebra, considering the prime congruences with respect to the term condition commutator. Then we use the topological structure of the minimal prime spectrum to study extensions of universal algebras that generalize certain types of ring extensions. Our results hold for semiprime members of semidegenerate congruence–modular varieties, as well as semiprime algebras whose term condition commutators are commutative and distributive with respect to arbitrary joins and satisfy certain conditions on compact congruences, even if those algebras do not generate congruence–modular varieties. |
| format | Article |
| id | doaj-art-15151c0690f64bbe8e105cbc69125a64 |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-15151c0690f64bbe8e105cbc69125a642025-08-20T02:55:35ZengMDPI AGAxioms2075-16802024-11-01131282410.3390/axioms13120824Congruence Extensions in Congruence–Modular VarietiesGeorge Georgescu0Leonard Kwuida1Claudia Mureşan2Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, RomaniaSchool of Business, Bern University of Applied Sciences, 3005 Bern, SwitzerlandFaculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, RomaniaWe investigate from an algebraic and topological point of view the minimal prime spectrum of a universal algebra, considering the prime congruences with respect to the term condition commutator. Then we use the topological structure of the minimal prime spectrum to study extensions of universal algebras that generalize certain types of ring extensions. Our results hold for semiprime members of semidegenerate congruence–modular varieties, as well as semiprime algebras whose term condition commutators are commutative and distributive with respect to arbitrary joins and satisfy certain conditions on compact congruences, even if those algebras do not generate congruence–modular varieties.https://www.mdpi.com/2075-1680/13/12/824(modular) commutator(minimal) prime congruence(Stone, Zariski, flat) topology(ring) extension |
| spellingShingle | George Georgescu Leonard Kwuida Claudia Mureşan Congruence Extensions in Congruence–Modular Varieties Axioms (modular) commutator (minimal) prime congruence (Stone, Zariski, flat) topology (ring) extension |
| title | Congruence Extensions in Congruence–Modular Varieties |
| title_full | Congruence Extensions in Congruence–Modular Varieties |
| title_fullStr | Congruence Extensions in Congruence–Modular Varieties |
| title_full_unstemmed | Congruence Extensions in Congruence–Modular Varieties |
| title_short | Congruence Extensions in Congruence–Modular Varieties |
| title_sort | congruence extensions in congruence modular varieties |
| topic | (modular) commutator (minimal) prime congruence (Stone, Zariski, flat) topology (ring) extension |
| url | https://www.mdpi.com/2075-1680/13/12/824 |
| work_keys_str_mv | AT georgegeorgescu congruenceextensionsincongruencemodularvarieties AT leonardkwuida congruenceextensionsincongruencemodularvarieties AT claudiamuresan congruenceextensionsincongruencemodularvarieties |