Adequate transversals of quasi-adequate semigroups

Adequate transversals of quasi-adequate semigroups

Al-Bar, Jehan and Renshaw, James (2009) Adequate transversals of quasi-adequate semigroups. Pre-print, 21pp. (Submitted)
http://eprints.soton.ac.uk/66452/

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Abstract

The concept of an adequate transversal of an abundant semigroup was introduced by El-Qallali in [5] whilst in [4] he and Fountain initiated the study of quasi-adequate semigroups as natural generalisations of orthodox semigroups. In this work we provide a structure theorem for adequate transversals of certain types of quasi-adequate semigroup and from this deduce Saito's classic result on the structure of inverse transversals of orthodox semigroups. We also apply it to left ample adequate transversals of left adequate semigroups and provide a structure for these based on semidirect products of adequate semigroups by left regular bands.

Item Type:	Article
ID Code:	66452
Uncontrolled Keywords:	abundant semigroup, adequate, quasi-adequate, left adequate, left ample, adequate transversal, semidirect product, inverse transversal, regular semigroup
Subjects:	Q Science > QA Mathematics
School or Centre:	School of Mathematics > Pure Mathematics
Deposited By:	Renshaw, Dr James
Deposited On:	10 July 2009

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References in Article

[1] Jehan Al-Bar & James Renshaw On adequate transversals, to appear in
Communications in Algebra.
[2] T.S. Blyth, `Inverse Transversals - A Guided Tour' in Proceedings of the International
Conference on Semigroups, Braga Portugal 18-23 June 1999, Ed. Paula Smith, Emilia
Giraldes, Paula Martins, World Scientic (2000) 26{43.
[3] Jianfei Chen, Abundant Semigroups with Adequate Transversals, Semigroup Forum,
Vol. 60 (2000) 67{79.
[4] A. El-Qallali and J.B. Fountain, Quasi-adequate semigroups, Proceedings of the Royal
Society of Edinburgh, 91A, 91{99, 1981.
[5] Abdulsalam El-Qallali, Abundant Semigroups with a multiplicative Type A transversal,
Semigroup Forum, Vol. 47 (1993) 327{340.
[6] John Fountain, Adequate Semigroups, Proceedings of the Edinburgh Mathematical
Society (1979), 22 113{125.
[7] John Fountain, Abundant Semigroups, Proc. London Math. Soc. 44 (1982), 103{129.
[8] Howie, J.M., Fundamentals of Semigroup Theory, London Mathematical Society
Monographs, (OUP, 1995).
[9] Tatsuhiki Saito, Construction of Regular Semigroups with Inverse Transversals,
Proceedings of the Edinburgh Mathematical Society (1989) 32, 41{51.
[10] Reikichi Yoshida, Left inverse semigroups with inverse transversals, Semigroup Forum
Vol. 33 (1986) 239{244.

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