On some classes of regular order semigroups
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Here, some classes of regular order semigroups are discussed.We shall consider that the problems of the existences of (multiplicative)inverse δpo-transversals for such classes of po-semigroups and obtain thefollowing main results: (1) Giving the equivalent conditions of the exis-tence of inverse δpo-transversals for regular order semigroups (2) showingthe order orthodox semigroups with biggest inverses have necessarily aweakly multiplicative inverse δpo-transversal. (3) If the Green’s relationR and L are strongly regular (see. sec.1), then any principally orderedregular semigroup (resp. ordered regular semigroup with biggest inverses)has necessarily a multiplicative inverse δpo-transversal. (4) Giving thestructure theorem of principally ordered semigroups (resp. ordered reg-ular semigroups with biggest inverses) on which R and L are stronglyregular.
Abstract
Here, some classes of regular order semigroups are discussed.We shall consider that the problems of the existences of (multiplicative)inverse δpo-transversals for such classes of po-semigroups and obtain thefollowing main results: (1) Giving the equivalent conditions of the exis-tence of inverse δpo-transversals for regular order semigroups (2) showingthe order orthodox semigroups with biggest inverses have necessarily aweakly multiplicative inverse δpo-transversal. (3) If the Green’s relationR and L are strongly regular (see. sec.1), then any principally orderedregular semigroup (resp. ordered regular semigroup with biggest inverses)has necessarily a multiplicative inverse δpo-transversal. (4) Giving thestructure theorem of principally ordered semigroups (resp. ordered reg-ular semigroups with biggest inverses) on which R and L are stronglyregular.
참고문헌 (7)
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