[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2009.24.4.481

ON REES MATRIX REPRESENTATIONS OF ABUNDANT SEMIGROUPS WITH ADEQUATE TRANSVERSALS

Gao, Zhen Lin (SCIENCE COLLEGE OF UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY)
Liu, Xian Ge (SCIENCE COLLEGE OF UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY)
Xiang, Yan Jun (SCIENCE COLLEGE OF UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY)
Zuo, He Li (SCIENCE COLLEGE OF UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY)

Publication Information

Communications of the Korean Mathematical Society / v.24, no.4, 2009 , pp. 481-500 More about this Journal

Abstract

The concepts of *-relation of a ( $\Gamma$ -)semigroup and $\bar{\Gamma}$ -adequate transversal of a ( $\Gamma$ -)abundant semigroup are defined in this note. Then we develop a matrix type theory for abundant semigroups. We give some equivalent conditions of a Rees matrix semigroup being abundant and some equivalent conditions of an abundant Rees matrix semigroup having an adequate transversal. Then we obtain some Rees matrix representations for abundant semigroups with adequate transversals by the above theories.

Keywords

abundant semigroup; adequate semigroup; adequate transversal; $\Gamma$ -adequate transversal;

Citations & Related Records

Times Cited By SCOPUS : 1

Reference

1	D. B. McAlister and R. B. McFadden, Semigroups with inverse transversals as matrix semigroups, J. Math. Oxford (2) 35 (1984), no. 140, 455–474 DOI
2	T. B. Blyth, Almeida, and M. H. Santos, On quasi-orthodox semigroups with inverse transversals, Proc. Edinburgh Math. Soc. 40 (1997), 505–514 DOI ScienceOn
3	T. K. Dutta and N. C. Adhikari, On Noetherian $\Gamma$ -semigroup, Kyungppok Math. J. 36 (1996), 85–95
4	N. K. Saha, The maximum idempotent-separating congruence on an inverse $\Gamma$ -semigroups, Kyungpook Math. J. 34 (1994,) no. 1, 59–66
5	M. K. Sen and N. K. Saha, On $\Gamma$ -semigroup I, Bull Calcutta Math. Soc. 78 (1986), 180–186
6	O. Steinfeld, On a generalization of completely 0-simple semigroups, Acta Sci. Math.(Szeged) 28 (1967), 135–145
7	A. EI-Qallali, On the construction of a class of abundant semigroups, Acta Math. Hung. 56 (1990), no. 1-2, 77–91 DOI
8	A. EI-Qallali, Abundant semigroups with a multiplicative type A transversal, Semigroup Forum 47 (1993), 327–340 DOI
9	J. Fountain, Abundant semigroups, Proc. Edinburgh Math. Soc. 22 (1979), 103–129
10	Z. L. Gao, On generalized abundant semigroups, (to appear)
11	J. M. Howie, An Introduction to Semigroup Theorem, Academic Press, London, 1976
12	A. EI-Qallali, Quasi-Adequate semigroups II, Semigroup Forum 44 (1992), 273–282 DOI