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ON SOME CLASSES OF REGULAR ORDER SEMIGROUPS
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 Title & Authors
ON SOME CLASSES OF REGULAR ORDER SEMIGROUPS
Gao, Zhenlin; Zhang, Guijie;
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 Abstract
Here, some classes of regular order semigroups are discussed. We shall consider that the problems of the existences of (multiplicative) inverse -transversals for such classes of po-semigroups and obtain the following main results: (1) Giving the equivalent conditions of the existence of inverse -transversals for regular order semigroups (2) showing the order orthodox semigroups with biggest inverses have necessarily a weakly multiplicative inverse -transversal. (3) If the Green`s relation and are strongly regular (see. sec.1), then any principally ordered regular semigroup (resp. ordered regular semigroup with biggest inverses) has necessarily a multiplicative inverse -transversal. (4) Giving the structure theorem of principally ordered semigroups (resp. ordered regular semigroups with biggest inverses) on which and are strongly regular.
 Keywords
regular order semigroup;inverse -transversals;POR-semigroups;ORB-semigroups;
 Language
English
 Cited by
 References
1.
T. S. Blyth and G. A. Pinto, On idempotent-generated subsemigroups of principally ordered regular semigroups, Semigroup Forum 65 (2003), 1-12 crossref(new window)

2.
T. S. Blyth and G. A. Pinto, Idempotents in principally ordered regular semigroups, Communications in Algebra 19 (1991), 1549-1563 crossref(new window)

3.
T. S. Blyth and G. A. Pinto, On ordered regular semigroup with biggest inverses, Semigroup Forum 54 (1997), 154-165 crossref(new window)

4.
T. S. Blyth and R. McFadden, Regular semigroups with a multiplicative inverse transversal, Proc. Rog. Soc. Edinburgh 92A (1982), 253-270

5.
Z. Gao, Naturally ordered abundant semigroups with adequate transversals, PU. M. A 14 (2003), no. 1-2, 35-50

6.
J. M. Howie, An Introduction to Semigroups Theory, Academic Press. London, 1976

7.
S. Tatsuhiko, Naturally ordered regular semigroups with maximum inverses, Roc. Edinburgh Math. Sec. 32 (1989), 33-39 crossref(new window)