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2013 | 33 | 2 | 201-209
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Nil-extensions of completely simple semirings

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EN
Abstrakty
EN
A semiring S is said to be a quasi completely regular semiring if for any a ∈ S there exists a positive integer n such that na is completely regular. The present paper is devoted to the study of completely Archimedean semirings. We show that a semiring S is a completely Archimedean semiring if and only if it is a nil-extension of a completely simple semiring. This result extends the crucial structure theorem of completely Archimedean semigroup.
Twórcy
  • Department of Mathematics, University of Burdwan, Golapbag, Burdwan - 713104, West Bengal, India
  • Department of Mathematics, University of Burdwan, Golapbag, Burdwan - 713104, West Bengal, India
Bibliografia
  • [1] S. Bogdanovic and S. Milic, A nil-extension of a completely simple semigroup, Publ. Inst. Math. 36 (50) (1984) 45-50.
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  • [4] J.S. Golan, The Theory of Semirings with Applications in Mathematics and Theoretical Computer Science (Pitman Monographs and Surveys in Pure and Applied Mathematics 54, Longman Sci. Tech., Harlow, 1992).
  • [5] U. Hebisch and J.H. Weinert, Semirings, Algebraic Theory and Applications in Computer Science, Series in Algebra Vol. 5 (World Scientific Singapore, 1998).
  • [6] J. M. Howie, Introduction to the Theory of Semigroups (Academic Press, 1976).
  • [7] N. Kehayopulu and K.P. Shum, Ideal extensions of regular poe-semigroups, Int. Math. J. 3 (2003) 1267-1277.
  • [8] S.K. Maity, Congruences in additive inverse semirings, Southeast Asian Bull. Math. 30 (3) (2001) 473-484.
  • [9] S.K. Maity and R. Ghosh, On quasi Completely Regular Semirings, (Accepted for publication in Semigroup Forum).
  • [10] C. Monico, On finite congruence-simple semirings, J. Algebra 271 (2004) 846-854. doi: 10.1016/j.jalgebra.2003.09.034.
  • [11] F. Pastijn and Y.Q. Guo, The lattice of idempotent distributive semiring varieties, Science in China (Series A) 42 (8) (1999) 785-804. doi: 10.1007/BF02884266
  • [12] F. Pastijn and X. Zhao, Varieties of idempotent semirings with commutative addition, Algebra Universalis 54 (3) (2005) 301-321. doi: 10.1007/s00012-005-1947-8
  • [13] M. Petrich and N.R. Reilly, Completely Regular Semigroups (Wiley, New York, 1999).
  • [14] M.K. Sen, S.K. Maity and K.P. Shum, Clifford semirings and generalized Clifford semirings, Taiwanese J. Math. 9 (3) (2005) 433-444.
  • [15] M.K. Sen, S.K. Maity and K.P. Shum, On completely regular semirings, Bull. Cal. Math. Soc. 88 (2006) 319-328.
  • [16] X. Zhao, K.P. Shum and Y.Q. Guo, 𝓛-subvarieties of the variety of idempotent semirings, Algebra Universalis 46 (1-2) (2001) 75-96. doi: 10.1007/PL00000348
  • [17] X. Zhao, Y.Q. Guo and K.P. Shum, 𝓓-subvarieties of the variety of idempotent semirings, Algebra of Colloqium 9 (1) (2002) 15-28.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1206
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