Download PDF - Clifford semifields
ArticleOriginal scientific text
Title
Clifford semifields
Authors 1, 1, 2
Affiliations
- Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata-700019, India
- Department of Mathematics, China, (SAR)
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
Bibliography
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- M.K. Sen, S.K. Maity and K.-P. Shum, Semisimple Clifford semirings, 'Advances in Algebra', World Scientific, Singapore, 2003, 221-231.
- M.K. Sen, S.K. Maity and K.-P. Shum, Clifford semirings and generalized Clifford semirings, Taiwanese J. Math., to appear.
- M.K. Sen, S.K. Maity and K.-P. Shum, On Completely Regular Semirings, Taiwanese J. Math., submitted.
- J. Zeleznekow, Regular semirings, Semigroup Forum, 23 (1981), 119-136.
Pages:
125-135
Main language of publication
English
Received
2003-12-31
Accepted
2004-07-12
Published
2004
DOI: 10.7151/dmgaa.1080
Exact and natural sciences