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全正则子半群构成链的正则半群(英文) 被引量：4

Regular Semigroups Whose Full Regular Subsemigroups Form a Chain
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摘要 本文考虑全正则子半群构成链的正则半群,得到了正则半群具有全正则子半群构成链的一个充分必要条件,这推广了Jones关于具有全正则子半群构成链的逆半群的结果.特别地,建立了具有全正则子半群构成链的完全0-单半群的结构. The main aim of this paper is to study regular semigroups whose full regular subsemigroups form a chain.We obtain a sufficient and necessary condition for a regular semigroup whose full regular subsemigroups form a chain.This extends the related result of Jones on inverse semigroups.In addition,the structure of completely 0-simple semigroups whose full regular subsemigroups form a chain is established.
作者 郭小江 Young Bae Jun
机构地区 江西师范大学数学系 Gyeongsang国立大学数学教育系
出处 《数学进展》 CSCD 北大核心 2011年第2期235-240,共6页 Advances in Mathematics（China）
基金 The research is supported by the NSFC(No.10961014) the NSF of Jiangxi Province the SF of Education Department of Jiangxi Province and the SF of Jiangxi Normal University.
关键词 正则半群 全正则子半群 格 链 regular semigroup full regular subsemigroup lattice chain
分类号 O152.7 [理学—基础数学]
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  • 1Sevrin, L.N. and Ovsyannikov, A.J., Semigroups and their subsemigroup lattice, Semigroup Forum, 1983, 27: 1-154.
  • 2Suzuki, M., Structure of a Group and the Structure of this Lattice of Subgroups, Berlin: Springer-Verlag, 1956.
  • 3Johnston, K.G., Subalgebra lattices of completely simple semigroups, Semigroup Forum, 1984, 29: 109-113.
  • 4Jones, P.R., Semimodular inverse semigroups, J. London Math. Soc., 1978, 17: 446-456.
  • 5Jones, P.R., Distriutive inverse semigroups, J. London Math. Soc., 1978, 17: 457-466.
  • 6Johnston, K.G., and Jones, P.R., The lattice of full regular subsemigroups of a regular semigroup, Proc. Royal Sac. Edinburgh, 1984, 98A: 203-214.
  • 7Tamura, T., On monoids whose submonoids form a chain, J. Gakugei Tokushima Univ., 1954, 5: 8-16.
  • 8Jones, P.R., Inverse semigroups whose full inverse subsemigroups form a chain, Glawgow Math. J., 1981, 22: 159-165.
  • 9Guo X.J., Huang F.S. and Shum, K.P., Type-A semigroups whose full regular subsemigroups form a chain under set inclusion, Asian-European J. Math., 2008, 1: 359-367.
  • 10Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups, Vol. I, Math. Survey of the American Math. Soc. 7, Provindence, R.I., 1961.

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数学进展
2011年 第2期

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