Algebras defined by equations
العنوان: | Algebras defined by equations |
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المؤلفون: | Marcel Jackson, Peter M. Higgins |
سنة النشر: | 2018 |
مصطلحات موضوعية: | Model theory, 0209 industrial biotechnology, Pure mathematics, Class (set theory), Algebra and Number Theory, Semigroup, Mathematics::Operator Algebras, 010102 general mathematics, 02 engineering and technology, Group Theory (math.GR), Mathematics - Logic, 16. Peace & justice, Elementary class, 01 natural sciences, Interpretation (model theory), 020901 industrial engineering & automation, Binary operation, FOS: Mathematics, 0101 mathematics, Algebraic number, Logic (math.LO), Mathematics - Group Theory, Associative property, Mathematics |
الوصف: | We show that an elementary class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular semigroups this allows an interpretation of a universal algebraic nature that is formulated entirely in terms of the associative binary operation of the semigroup, which serves as an alternative to the approach via so called e-varieties. In particular we prove that classes of Inverse semigroups, Orthodox semigroups, and E-solid semigroups are equational in our sense. We also examine which equations are valid in every semigroup. |
اللغة: | English |
URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::715f9470e117211a837d852ad531c461 http://arxiv.org/abs/1810.13012 |
حقوق: | OPEN |
رقم الأكسشن: | edsair.doi.dedup.....715f9470e117211a837d852ad531c461 |
قاعدة البيانات: | OpenAIRE |
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