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群的正则带的KG-强半格分解 被引量：1

KG-strong Semilattice Decomposition of Regular Cryptogroups
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摘要 推广了著名的Petrich的完全正则半群为群的正规带当且仅当它为完全单半群的强半 格的结果,证明了完全正则半群为群的正则(或右拟正规)带当且仅当它是完全单半群的HG(LG)- 强半格. The famous result of Petrich, a completely regular semigroup is a normal cryptogroup if and only if it is a strong semilattice of completely simple semigroups is generalized, we prove that a completely regular semigroup is a regular(or right quasinormal) cryptogroup if and only if it is an HG(LG)- strong semilattice of completely simple semigroups.
作者 孔祥智 袁志玲
机构地区 曲阜师范大学数学科学学院
出处 《数学进展》 CSCD 北大核心 2004年第6期697-702,共6页 Advances in Mathematics（China）
基金 曲阜师范大学青年基金资助(No.XJ02003 No.XJ03004).
关键词 KG-强半格分解 正则带 同余 同态 <Keyword>-strong semilattice decomposition regular band congruence homomor-phism
分类号 O152.7 [理学—基础数学]
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参考文献9

  • 1Putcha M S, Yakub. Band decomposition of semigroups [J]. Proc. Amer. Math. Soc., 1972, 33: 1-7.
  • 2Putcha M S, Weissglas J. A semilattice decomposition into semigroups having at most one idempotent [J].Pacific J. Math., 1971, 39: 225-228.
  • 3Petrich M, Reilly N R. Completely Regular Semigroups [M]. New York: John Wiley & Sons, Inc, 1999.
  • 4Petrich M. Introduction to Semigroups [M]. Merrill: Columbus, 1973.
  • 5Xiang Zhi KONG,Department of Mathematics, Zhengzhou University. Zhengzhou 450052, P. R. China Department of Mathematics, Qufu Normal University, Qufu 273165. P. R. China.On the Construction of Regular Orthocryptogroups[J].Acta Mathematica Sinica,English Series,2002,18(3):517-530. 被引量：2
  • 6Kong Xiangzhi, Shum K P. On the structure of regular crypto semigroups [J]. Comm. Algebra, 2001, 29(6):2461-2479.
  • 7孔祥智,袁志玲.正则带的半格结构[J].数学进展,2002,31(5):476-482. 被引量：4
  • 8Howie J M. An Introduction to Semigroup Theory [M]. London: Academic Press, 1976.
  • 9Petrich M. Lectures in Semigroups [M]. Berlin: John Wiley & Sons, Academic-Verlag, 1977.

二级参考文献10

  • 1[1]Howie J M. An Introduction to Semigroup Theory. London: Academic Press, 1976.
  • 2[2]Petrich M and Reilly N R. Completely Regular Semigroups. New York: John Wiley & Sons, Inc, 1999.
  • 3[3]Yamada M and Kimura N. Note on idempotent semigroups, II. Proc. Japan. Acad, 1958, 34: 110-112.
  • 4[4]Petrich M. Lectures in Semigroups. Berlin: Academic Verlag, 1977.
  • 5[5]Zhang Liang, Shum Karping and Zhang Ronghua. On refined semilattices, to appear in Algebra Colloquium.
  • 6[6]Kong Xiangzhi and Shum Karping. On the structure of regular crypto semigroups. Communications in Algebra, 2001, 29(6): 2461-2479.
  • 7Petrich M.Lectures in semigroups[]..1977
  • 8Petrich M,Reilly N R.Completely Regular Semigroups[]..1999
  • 9Petrich,M.A construction and a classification of bands[].Math Nochrchten.1971
  • 10Zhang, L,Huang. J.General semilattice of semigroups type T and the structure of regular bands[].The Proc of Kunming conference’’ in semigroups.1998

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数学进展
2004年 第6期

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