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Discussiones Mathematicae General Algebra and Applications 24(1) (2004) 125-135
DOI: https://doi.org/10.7151/dmgaa.1080

CLIFFORD SEMIFIELDS

Mridul K. Sen and Sunil K. Maity Department of Pure Mathematics, University of Calcutta 35, Ballygunge Circular Road, Kolkata-700019, India e-mails: senmk@cal3.vsnl.net.in, sskmaity@yahoo.com

Kar-Ping Shum Department of Mathematics China, (SAR) e-mail: kpshum@math.cuhk.edu.hk

Abstract

It is well known that a semigroup S is a Clifford semigroup if and only if S is a strong semilattice of groups. We have recently extended this important result from semigroups to semirings by showing that a semiring S is a Clifford semiring if and only if S is a strong distributive lattice of skew-rings. In this paper, we introduce the notions of Clifford semidomain and Clifford semifield. Some structure theorems for these semirings are obtained.

Keywords: skew-ring, Clifford semiring, Clifford semidomain, Clifford semifield, Artinian Clifford semiring.

2000 Mathematics Subject Classification: 16Y60, 20N10, 20M07, 12K10.

References

[1]	D.M. Burton, A First Course in Rings and Ideals, Addison-Wesley Publishing Company, Reading, MA, 1970.
[2]	M.P. Grillet, Semirings with a completely simple additive semigroup, J. Austral. Math. Soc. (Series A) 20 (1975), 257-267.
[3]	P.H. Karvellas, Inverse semirings, J. Austral. Math. Soc. 18 (1974), 277-288.
[4]	M.K. Sen, S.K. Maity and K.-P. Shum, Semisimple Clifford semirings, p. 221-231 in: ``Advances in Algebra'', World Scientific, Singapore, 2003.
[5]	M.K. Sen, S.K. Maity and K.-P. Shum, Clifford semirings and generalized Clifford semirings, Taiwanese J. Math., to appear.
[6]	M.K. Sen, S.K. Maity and K.-P. Shum, On Completely Regular Semirings, Taiwanese J. Math., submitted.
[7]	J. Zeleznekow, Regular semirings, Semigroup Forum, 23 (1981), 119-136.

Received 31 December 2003
Revised 12 July 2004