关于P-主弱内射系的特征

doi:10.6040/j.issn.1671-9352.0.2021.694

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (10): 6-10.doi: 10.6040/j.issn.1671-9352.0.2021.694

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关于P-主弱内射系的特征

乔虎生,袁莹民^*

西北师范大学数学与统计学院, 甘肃兰州 730070

发布日期:2022-10-06
作者简介:乔虎生(1974— ), 男, 博士, 教授, 博士生导师, 研究方向为半群代数理论. E-mail:gsqiaohsh@163.com*通信作者简介:袁莹民(1997— ), 女, 硕士研究生, 研究方向为半群代数理论. E-mail:2316679859@qq.com
基金资助:
国家自然科学基金资助项目(11961058)

On the characterizations of P-principally weakly injective acts

QIAO Hu-sheng, YUAN Ying-min^*

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Published:2022-10-06

摘要/Abstract

摘要： 设S是幺半群, P是S的非空子集。基于P中任意元素生成的主右理想的嵌入定义的一类新的主弱内射系, 称之为P-主弱内射系。利用这类新的性质给出了一些新的幺半群类的刻画。

关键词: S-系, P-主弱内射, 主弱内射

Abstract: Let S be a monoid and P be a nonempty subset of S. A new kind of principally weakly injective act is defined, which is based on the embedding principal right ideals generated by elements in P and is called P-principally weakly injective act. Using this new property, the characterizations of some new classes of monoids are given.

Key words: S-act, P-principally weakly injective, principally weakly injective

中图分类号:

O152.7

乔虎生,袁莹民. 关于P-主弱内射系的特征[J]. 《山东大学学报(理学版)》, 2022, 57(10): 6-10.

QIAO Hu-sheng, YUAN Ying-min. On the characterizations of P-principally weakly injective acts[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 6-10.

参考文献

[1] 乔虎生, 刘仲奎. 半群引论[M]. 北京: 科学出版社, 2019. QIAO Husheng, LIU Zhongkui. An introduction to semigroups[M]. Beijing: Science Press, 2019.
[2] KILP M, KNAUER U, MIKHALEV A V. Monoids, acts and categories[M] //De Gruyter Expositions in Mathematics, 29. Berlin: De Gruyter Mouton, 2000.
[3] QIAO Husheng, YIN Haiyan. On a new kind of principally weakly injective acts over monoids[J]. Journal of Lanzhou University(Natural Sciences), 2013, 49(5):715-718.
[4] 刘仲奎, 乔虎生. 半群的S-系理论[M]. 北京: 科学出版社, 2008. LIU Zhongkui, QIAO Husheng. The S-act theory of semigroups[M]. Beijing: Science Press, 2008.
[5] GOULD V. Divisiable S-systems and R-modules[J]. Proceedings Edinburgh Mathematics Society, 1987, 30(2):187-200.
[6] ZHANG Xia, KNAUER U, CHEN Yuqun. Various notions of weak injectivity over Clifford semigroups[J]. Semigroups Forum, 2008, 76(2):357-367.

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关于P-主弱内射系的特征

On the characterizations of P-principally weakly injective acts

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