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序半群的一类正则同余 被引量：2

A Class of Regular Congruences on Ordered Semigroups
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摘要 设S是有向序半群,本文给出了S上的一类正则同余,称为强序同余的定义及性质.证明了S的强序同余是强正则同余,但反之不成立.同时证明了强序同余格SOC(S)是S的同余格C(S)关于通常集合的交和传递积的V-完备的分配子格. In this paper, the notation of a strongly ordered congruence on an ordered semigroup S is introduced. Some properties of strongly ordered congruences are given. The results that the strongly ordered congruences are the strongly regular congruences and that the converses are not true are proved. In the Section 3, we also prove that the set SOC（S） of all strongly ordered congruences on an ordered semigroup S is a V-complete distributive sublattice of the lattice C（S） of all congruences on S with respect to the intersection defined as usual and the union （also called transitive product）.
作者 谢祥云 郭小江
机构地区 五邑大学数理系 江西师范大学数学与信息科学学院
出处 《数学进展》 CSCD 北大核心 2007年第4期459-466,共8页 Advances in Mathematics（China）
基金 国家自然科学基金 广东省自然科学基金(No.0501332).
关键词 有向序半群 强序同余 正则同余 分配格 directed ordered semigroup strongly ordered congruence regular congruence distributive lattice
分类号 O152.7 [理学—基础数学]
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参考文献12

  • 1Fuchs,L.,On group homomorphic images of partially ordered semigroups,Acta Sci.Math.,1964,25:139-142.
  • 2McCarthy,P.J.,Homomorphisms of certain commutative lattice-ordered semigroup,Acta Sci.Math.,1966,27:63-65.
  • 3Blyth,T.S.and Janowitz,M.F.,Residuation Theory,Pergamon Press,1972.
  • 4Kehayopulu,N.& Tsingelis,M.,On subdirectly irreducible ordered semigroups,Semigroup Forum,1995,50:161-177.
  • 5Kehayopulu,N.& Tsingelis,M.,Pseudoorder in ordered semigroups,Semigroup Forum,1995,50:389-392.
  • 6Xie X-Y.,Contributions to theory of congruences on ordered semigroups,Doctoral Dissertation,Lanzhou University,1995.
  • 7Xie X-Y.,On congruences on ordered semigroups,J.Math.& Res.Expo.,2001,21:207-214.
  • 8Xie X -Y.,Remarks on regular congruences on po-semigroups,SEA Bull.Math.,2000,24:661-666.
  • 9Xie X -Y.,On regular,strongly regular congruences ordered semigroups,Semigroup Forum,2000,61:159-178.
  • 10Xie X -Y.,Wu M -F.,On congruences on ordered semigroups,Math.Japonica,1997,45:81-85.

同被引文献15

  • 1郭小江,罗彦锋.富足半群上的自然偏序(英文)[J].数学进展,2005,34(3):297-308. 被引量：21
  • 2Guo Xiaojiang, Shum K P. On translational hulls of type-A semigroups[J]. J Algebra, 2003,269 (1) : 240.
  • 3Howie J M. An introduction to semigroup theory[M]. London:Acad Press, 1976.
  • 4Li Hongwei. The translational hulls of Rees matrix semigroups over monoids[J]. Southeast Asian Bull of Math,2010,34 (2) :309.
  • 5Petrich M. The translational hull in semigroups and rings[J]. Semigroup Forum, 1970,1 (1):283.
  • 6Howie J M. An Introduction to Semigroup Theory[M]. Acad, Press London, New York, 1976.
  • 7Ponizovski I S. A Remark on Inverse Semigroups[J]. Usp Math Nauk, 1965, 20: 147-148.
  • 8Xiaojiang Guo and Shum K P. On Translational Hulls of Type-A Semigroups[J]. Journal of Algebra, 2003, 269: 240-249.
  • 9Petrich M. The translational hull in semigroups and rings[J]. Semigroup Forum, 1970, 1: 283-360.
  • 10Hongwei Li. The translational hulls of rees matrix semigroups over monoids[J]. Southeast Asian Bulletin of Mathematics, 2010, 34(2): 309-320.

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数学进展
2007年 第4期

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