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M.Petrich和N.R.Reilly一个问题的证明 被引量:1

A solution on a problem of M.Petrich and N.R.Reilly
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摘要 证明了M.Petrich和N.R.Reilly关于完全正则半群上纯整同余的核的一个公开问题,讨论何种情况下纯整同余的核是群带.并给出其同余核上Green关系H为同余的一个表示. In this paper a problem of M. Petrich and N. R. Reilly is considered. If μ is orthodox, is kerμ cryptic (μ is the maximum idempotent-separating congruence)? Show that if some conditions are satisfied, the kernel of an orthodox congruence is cryptic.
出处 《纯粹数学与应用数学》 CSCD 北大核心 2005年第2期151-153,171,共4页 Pure and Applied Mathematics
基金 曲阜师范大学基金资助项目(XJ02003)(XJ03004).
关键词 纯整同余 群带 orthodox congruence, kernel, cryptic
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参考文献5

  • 1Petrich M and Reilly N R. Completely Regular Scmigroups[M]. New York: Wiley, 1999.
  • 2Trotter P G. The least orthodox congruence on a completely regular semigroup[J]. Indian J. Math.,1983, 25:125~133.
  • 3Howie J M. An Introduction to Semigroup Theory[M].London: Academic Press, 1976.
  • 4Araújo I M, Branco M J J, etc. On generations and relations for unions of semigroups[J]. Semigroup Forum,2001, 63:49~62.
  • 5Kong Xiangzhi and Shum K P. On the structure of regular crypto semigroups[J]. Communications in Algebra,2001, 29(6):2461~2479.

同被引文献5

  • 1Trotter P G.The least orthodox congruence on a completely regular semigroup[J].Indian J Math,1983,25:125-133.
  • 2Petrich M,Reilly N R.Completely Regular Semigroups[M].New York:John Wiley & Sons Inc,1999.
  • 3Howie J M.An Introduction to Semigroup Theory[M].London:Academic Press,1976.
  • 4Pastijn F J,Petrich M.The congruence lattice of a regular semigroup[J].J Pure App Algebra,1988,53..93-123.
  • 5Gomes M S.Orhthodox congruences on regular semigroups[J].Semigroup Forum,1988,37:148-166.

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