ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications


Discussiones Mathematicae General Algebra and Applications 24(1) (2004) 125-135


Mridul K. Sen and Sunil K. Maity

Department of Pure Mathematics, University of Calcutta
35, Ballygunge Circular Road, Kolkata-700019, India


Kar-Ping Shum

Department of Mathematics
China, (SAR)



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.


[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