ABUNDANT SEMIGROUPS WITH QUASI-IDEAL S-ADEQUATE TRANSVERSALS

Title & Authors
ABUNDANT SEMIGROUPS WITH QUASI-IDEAL S-ADEQUATE TRANSVERSALS
Kong, Xiangjun; Wang, Pei;

Abstract
In this paper, the connection of the inverse transversal with the adequate transversal is explored. It is proved that if S is an abundant semigroup with an adequate transversal $\small{S^o}$, then S is regular if and only if $\small{S^o}$ is an inverse semigroup. It is also shown that adequate transversals of a regular semigroup are just its inverse transversals. By means of a quasi-adequate semigroup and a right normal band, we construct an abundant semigroup containing a quasi-ideal S-adequate transversal and conversely, every such a semigroup can be constructed in this manner. It is simpler than the construction of Guo and Shum [9] through an SQ-system and the construction of El-Qallali [5] by W(E, S).
Keywords
Language
English
Cited by
1.
CONGRUENCES ON ABUNDANT SEMIGROUPS WITH QUASI-IDEAL S-ADEQUATE TRANSVERSALS,;;

대한수학회논문집, 2014. vol.29. 1, pp.1-8
1.
CONGRUENCES ON ABUNDANT SEMIGROUPS WITH QUASI-IDEAL S-ADEQUATE TRANSVERSALS, Communications of the Korean Mathematical Society, 2014, 29, 1, 1
2.
Good congruences on abundant semigroups with \$\$PSQ\$\$ P S Q -adequate transversals, Semigroup Forum, 2014, 89, 2, 462
3.
The product of quasi-ideal adequate transversals of an abundant semigroup, Semigroup Forum, 2011, 83, 2, 304
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