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On Monoids over which All Strongly Flat Right S-Acts Are Regular 被引量：2

关于所有强平坦右S-系是正则系的幺半群(英文)
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摘要 This paper investigates the characterizations of monoids over which all strongly flat right S-acts are regular. It is shown that all strongly flat right S-acts are regular if and only if S is a right PSF monoid and every left collapsible submonoid of S contains a left zero. This result gives a new answer to the problem in Kilp and Knauer. 本论文考虑了所有强平坦右S-系是正则系的幺半群的刻画,证明了所有强平坦右S-系是正则S-系当且仅当S是右PSF幺半群并且S的每一个左coilpasible子幺半群包含左零元．该结果对Kilp和Knauer在文献[7]中的问题给出了一个新的回答．
作者 乔虎生
机构地区 西北师范大学数学与信息科学学院
出处 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2006年第4期720-724,共5页 数学研究与评论（英文版）
基金 the National Natural Science Foundation of China(10171082)and by NWNU-KJCXGC212
关键词 strong fiat S-acts regular S-acts. 强平坦S-系 正则S-系
分类号 O152.7 [理学—基础数学]
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参考文献12

  • 1WANG Ning, LIU Zhong-kui. Monoids over which aJl strongly fiat left acts are regular [J]. Comm. Algebra, 1998, 26(6): 1863-1866.
  • 2KILP M.On monoids over which all strongly fiat cyclic right acts are projective [J]. Semigroup Forum, 1996,52: 241-245.
  • 3STENSTROM B. Flatness and Localization over monoids [J]. Math. Nachr., 1971, 48: 315-334.
  • 4KNAUER U. Projectivity of acts and Morita equivalence ofmonoids [J]. Semigroup Forum, 1972, 3: 359-370.
  • 5BULMAN-FLEMING S, NORMAK P. Monoids over which all fiat cyclic right acts are strongly fiat [J]. Semigroup Forum, 1995, 50: 233-241.
  • 6KNAUER U. Characterization of Monoids by Properties of Finitely Cenerated Right Acts and Their Right Ideals [M]. Lecture Notes in Math., 998, Springer, Berlin, 1983.
  • 7KILP M,KNAUER U. Characterization of monoids by properties of regular acts [J]. J. Pure Appl. Algebra, 1987, 46: 217-231.
  • 8TRNLAM H. Characterization of monoids by regular acts [J]. Period. Math. Hungar, 1985, 16: 273-279.
  • 9KNAUER U, MIKHALEV A V. Wreath products of acts over monoids. I. Regular and inverse acts [J]. J. Pure Appl. Algebra, 1988, 51: 251-260.
  • 10LIU Zhong-kui, YANG Yong-bao. Monoids over which every fiat right act satisfies condition (P) [J]. Comm. Algebra, 1994, 22(8): 2861-2875.

同被引文献6

  • 1魏加群.某些左S-系之间关系的刻划[J].南京师大学报（自然科学版）,2005,28(1):8-10. 被引量：1
  • 2KILP M, KNAUER U. Characterization of monoids by properties of regular acts [J]. J Pure Appl Algebra, 1987, 46: 217- 321.
  • 3BULMAN-FLEMING S. Flat and strongly flat S-systems [J]. Comm in Algebra, 1992,20(9) : 2553-2567.
  • 4LIU Z K. Monoids over which all flat left acts are regular [J]. J Pure .Appl Algebra, 1996,111 : 199-203.
  • 5BULMAN-FLEMING S, NORMAK P. Monoids over which all flat cyclic right acts are strongly flat [J]. Semigroup Forum, 1995,50:233-241.
  • 6赵华,宋桂安.条件(wR)对幺半群的刻画[J].解放军理工大学学报（自然科学版）,2003,4(6):101-102. 被引量：1

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二级引证文献1

Journal of Mathematical Research and Exposition
2006年 第4期

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