Abstract
SynopsisThe existence of a smallest inverse congruence on an orthodox semigroup is known. It is also known that a regular semigroup S is locally inverse and orthodox if and only if there exists a local isomorphism from S onto an inverse semigroup T.In this paper, we show the existence of a smallest R-unipotent congruence ρ on an orthodox semigroup S and give its expression in the case where S is also left quasinormal. Finally, we prove that a regular semigroup S is left quasinormal and orthodox if and only if there exists a local isomorphism from S onto an R-unipotent semigroup T.
Publisher
Cambridge University Press (CUP)
Reference18 articles.
1. The minimum group congruence on an ℒunipotent semigroup
2. Coextensions of regular semigroups by rectangular bands I;Meakin;Trans. Amer. Math. Soc.,1982
3. Congruences on Orthodox Semigroups
4. 8 McAlister D. B. . Rees matrix covers for locally inverse semigroups, (to appear).
5. Regular semi-groups whose idempotents satisfy permutation identities
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献