ON SOME CLASSES OF REGULAR ORDER SEMIGROUPS

Title & Authors
ON SOME CLASSES OF REGULAR ORDER SEMIGROUPS
Gao, Zhenlin; Zhang, Guijie;

Abstract
Here, some classes of regular order semigroups are discussed. We shall consider that the problems of the existences of (multiplicative) inverse $\small{^{\delta}po}$-transversals for such classes of po-semigroups and obtain the following main results: (1) Giving the equivalent conditions of the existence of inverse $\small{^{\delta}po}$-transversals for regular order semigroups (2) showing the order orthodox semigroups with biggest inverses have necessarily a weakly multiplicative inverse $\small{^{\delta}po}$-transversal. (3) If the Green's relation $\small{\cal{R}}$ and $\small{\cal{L}}$ are strongly regular (see. sec.1), then any principally ordered regular semigroup (resp. ordered regular semigroup with biggest inverses) has necessarily a multiplicative inverse $\small{^{\delta}po}$-transversal. (4) Giving the structure theorem of principally ordered semigroups (resp. ordered regular semigroups with biggest inverses) on which $\small{\cal{R}}$ and $\small{\cal{L}}$ are strongly regular.
Keywords
regular order semigroup;inverse $\small{^{\delta}po}$-transversals;POR-semigroups;ORB-semigroups;
Language
English
Cited by
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