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Clifford semifields

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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.
Twórcy
  • Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata-700019, India
  • Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata-700019, India
  • Department of Mathematics, China, (SAR)
Bibliografia
  • [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, 'Advances in Algebra', World Scientific, Singapore, 2003, 221-231.
  • [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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1080
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