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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.
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참고문헌 (7)
참고문헌 신청
J. M. Howie / 1976 / An Introduction to Semigroups Theory / Academic Press
S. Tatsuhiko / 1989 / Naturally ordered regular semigroups with maximum inverses / Roc. Edinburgh Math. Sec 32 : 33 ~ 39
T. S. Blyth / 1982 / Regular semigroups with a multiplicative inverse transversal / Proc. Rog. Soc. Edinburgh 92A : 253 ~ 270
T. S. Blyth / 1991 / Idempotents in principally ordered regular semigroups / Communications in Algebra 19 : 1549 ~ 1563
T. S. Blyth / 1997 / On ordered regular semigroup with biggest inverses / Semigroup Forum 54 : 154 ~ 165
S. Tatsuhiko / 1989 / Naturally ordered regular semigroups with maximum inverses / Roc. Edinburgh Math. Sec 32 : 33 ~ 39
T. S. Blyth / 1982 / Regular semigroups with a multiplicative inverse transversal / Proc. Rog. Soc. Edinburgh 92A : 253 ~ 270
T. S. Blyth / 1991 / Idempotents in principally ordered regular semigroups / Communications in Algebra 19 : 1549 ~ 1563
T. S. Blyth / 1997 / On ordered regular semigroup with biggest inverses / Semigroup Forum 54 : 154 ~ 165
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