CONGRUENCES ON ABUNDANT SEMIGROUPS WITH QUASI-IDEAL S-ADEQUATE TRANSVERSALS

Title & Authors
CONGRUENCES ON ABUNDANT SEMIGROUPS WITH QUASI-IDEAL S-ADEQUATE TRANSVERSALS
Wang, Lili; Wang, Aifa;

Abstract
In this paper, we give congruences on an abundant semigroup with a quasi-ideal S-adequate transversal $\small{S^{\circ}}$ by the congruence pair abstractly which consists of congruences on the structure component parts R and $\small{{\Lambda}}$. We prove that the set of all congruences on this kind of semigroups is a complete lattice.
Keywords
Language
English
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References
1.
T. S. Blyth and R. B. McFadden, Regular semigroups with a multiplicative inverse transversal, Proc. Roy. Soc. Edinburgh Sect. A 92 (1982), no. 3-4, 253-270.

2.
J. F. Chen, Abundant semigroups with adequate transversals, Semigroup Forum 60 (2000), no. 1, 67-79.

3.
A. El-Qallali, Abundant semigroups with a multiplicative type A transversal, Semigroup Forum 47 (1993), no. 3, 327-340.

4.
J. B. Fountain, Adequate semigroups, Proc. Edinburgh Math. Soc. 22 (1979), no. 2, 113-125.

5.
J. B. Fountain, Abundant semigroups, Proc London Math. Soc. 44 (1982), no. 1, 103-129.

6.
X. J. Guo, Abundant semigroups with a multiplicative adequate transversal, Acta Math. Sin 18 (2002), no. 2, 229-244.

7.
X. J. Guo and L. M. Wang, Idempotent-connected abundant semigroups which are disjoint unions of quasi-ideal adequate transversals, Comm. Algebra 30 (2002), no. 4, 1779-1800.

8.
X. J. Kong and P. Wang, Abundant semigroups with quasi-ideal S-adequate transversals, Commun. Korean Math. Soc. 26 (2011), no. 1, 1-12.

9.
X. L. Tang, Regular semigroups with inverse transversals, Semigroup Forum 55 (1997), no. 1, 24-32.

10.
X. L. Tang and L. M. Wang, Congruences on regular semigroups with inverse transversals, Comm. Algebra 23 (1995), no. 11, 4157-4171.

11.
L. M. Wang, On congruence lattice of regular semigroups with Q-inverse transversals, Semigroup Forum 50 (1995), no. 2, 141-160.

12.
L. M. Wang and X. L. Tang, Congruence lattices of regular semigroups with inverse transversals, Comm. Algebra 26 (1998), no. 4, 1234-1255.