G-generalized Completely Regular Semigroup A Number Of Studies

The main topics of this paper are properties, structures of some kinds of G-generalized completely regular semigroups and their subclasses, and congruences on them. Firstly, based on the semilattice decomposition of ortho-lc-monoids ob-tained by Y. Q. Guo etc., some structure theorems for ortho-lc-monoids are estab-lished. As direct corollaries of the results which we obtained, some new structure theorems for ortho-c-monoids and orthogroups are given. Moreover, some special ortho-lc-monoids such as orthocrypto-lc-monoids, lc-Clifford semigroups are defined and studied, in particular, their structures are characterized, the semilattice de-composition of super-r-ample semigroups is given. Secondly, by means of the semi-spined product structure of regular ortho-lc-monoids obtained by Y. Q. Guo etc. the (*,-)-good congruences on regular ortho-lc-monoids are characterized. Thirdly, orthogroups are further generalized in the class of E(S)-semiabundant semigroups. By means of (-)-Green's relations, super E(S)-semiabundant semigroups and ortho-u-monoids are defined and investigated. Moreover, the semilattice decomposition of ortho-u-monoids and a structure theorem for regular ortho-u-monoids are obtained. Lastly, a structure theorem for completely (?)*,--simple semigroups are established by using Rees matrix semigroups over left cancellative monoids.