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山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (10): 1-3.doi: 10.6040/j.issn.1671-9352.0.2017.037

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关于正则系是弱内射系的幺半群

乔虎生,金文刚   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 收稿日期:2017-02-10 出版日期:2017-10-20 发布日期:2017-10-12
  • 作者简介:乔虎生(1974— ), 男, 博士, 教授, 研究方向为半群代数理论. E-mail:qiaohs@nwnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11461060);甘肃省高校基本科研业务费

On monoids over which all weakly injective right S-acts are regular

QIAO Hu-sheng, JIN Wen-gang   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2017-02-10 Online:2017-10-20 Published:2017-10-12

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摘要： 设S是幺半群。 研究了所有正则右S-系是弱内射系的幺半群的特征,纠正了Moon给出的错误结论, 并讨论了正则系是fgdu-弱内射S-系的幺半群的等价刻画。

关键词: fgdu-弱内射S-系, 正则系, 弱内射S-系

Abstract: Let S be a monoid. The characterizations of monoids over which all weakly injective right S-acts are regular is investigated, some wrong results of Moon are corrected. Moreover, the equivalent characterization of monoids over which all fgdu-weakly injective right S-acts are regular are obtained.

Key words: weakly injective S-act, regular act, fgdu-weakly injective S-act

中图分类号: 

  • O152.7
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[2] KLIP M, KNAUER U, Mikhalev A V. Monoids, acts, and categories[M]. Berlin: Walter de Gruyter, 2000.
[3] LIU Zhongkui. Monoids over which all regular left acts are flat[J]. Semigroup Forum, 1995, 50:135-139.
[4] HACH T L. Characterization of monoids by regular acts[J]. Period Sci Math Hung, 1985, 16:273-279.
[5] KLIP M, KNAUER U. Characterization of monoids by properties of regular acts[J]. Journal of Pure and Applied Algebra, 1987, 46:217-231.
[1] 金萌. 正则与简单系统算法的优化[J]. J4, 2010, 45(12): 106-111.
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