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Universal varieties of semigroups
| Content Provider | Scilit |
|---|---|
| Author | Koubek, V. Sichler, J. |
| Copyright Year | 1984 |
| Description | A category V is called universal (or binding) if every category of algebras is isomorphic to a full subcategory of V. The main result states that a semigroup variety V is universal if and only if it contains all commutative semigroups and fails the identity $x^{n}y^{n}$ = $(xy)^{n}$ for every n ≥ 1. Further-more, the universality of a semigroup variety V is equivalent to the existence in V of a nontrivial semigroup whose endomorphism monoid is trivial, and also to the representability of every monoid as the monoid of all endomorphisms of some semigroup in V. Every universal semigroup variety contains a minimal one with this property while there is no smallest universal semigroup variety. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A6202E884A1D86CFC16DA495AFAFE4EB/S1446788700024617a.pdf/div-class-title-universal-varieties-of-semigroups-div.pdf |
| Ending Page | 152 |
| Page Count | 10 |
| Starting Page | 143 |
| ISSN | 02636115 |
| DOI | 10.1017/s1446788700024617 |
| Journal | Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics |
| Issue Number | 2 |
| Volume Number | 36 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1984-04-01 |
| Access Restriction | Open |
| Subject Keyword | Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics Primary 18 B 15 20 M 07 Secondary 20 M 15 08 A 35. |
| Content Type | Text |
| Resource Type | Article |
