The Structure of Ortho-LC-Monoids
Chunmei Gong, Y. Q. Guo, Xiaoming Ren · Communications in Algebra · 2011
The super-r-wide semigroups (in [6 Guo , Y. Q. , Shum , K. P. , Gong , C. M. ( 2011 ). On (*, ∼)-Green's relations and ortho-lc-monoids . Communications in Algebra 39 : 5 – 31 .[Taylor & Francis Online] , [Google Scholar]], called super-r-ample semigroups) [ortho-lc-monoids] within the class of rpp semigroups form a kind of generalized completely regular semigroups [orthogroups]. In this article, some structure theorems of ortho-lc-monoids are established and some special ortho-lc-monoids such as orthocrypto-lc-monoids, lc-Clifford semigroups, which we defined, are considered; the semilattice decomposition of super-r-wide semigroups is given. As direct corollaries of the results that we obtained, some new structure theorems for ortho-c-monoids and orthogroups, different from [10, 13], are given, and hence, the structure theorem for ortho-lc-monoids that we established is not the direct generalization of the results in [10 Petrich , M. ( 1987 ). A structure theorem for completely regular semigroups . Proc. Amer. Math. Soc. 99 : 617 – 622 .[Crossref], [Web of Science ®] , [Google Scholar], 13 Ren , X. M. , Shum , K. P. ( 2007 ). On superabundant semigroups whose set of idempotents form a subsemigroup . Algebra Colloquium 14 : 215 – 228 .[Crossref], [Web of Science ®] , [Google Scholar]]; the structure of orthocryptogroups is reobtained; the well-known Clifford theorem is further generalized.