K-分离性质对幺半群的刻画

doi:10.6040/j.issn.1671-9352.0.2021.523

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (6): 31-35.doi: 10.6040/j.issn.1671-9352.0.2021.523

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K-分离性质对幺半群的刻画

王雅婷,乔虎生^*

西北师范大学数学与统计学院, 甘肃兰州 730070

发布日期:2022-06-10
作者简介:王雅婷(1998— ), 女, 硕士研究生, 研究方向为半群代数理论. E-mail:1400461512@qq.com*通信作者简介: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
基金资助:
国家自然科学基金资助项目(11961058)

Characterizations of monoids by K-separation property

WANG Ya-ting, QIAO Hu-sheng^*

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

Published:2022-06-10

摘要/Abstract

摘要： 设S是幺半群,K是S的任意非空子集,研究了Rees商和融合余积的K-分离性质,给出了拉回图对K-分离性质的刻画,并且讨论了K-分离性质关于自由(投射,主弱平坦)Rees商S-系的同调分类问题。

关键词: K-分离, 主弱平坦, 挠自由

Abstract: Let S be a monoid, K be an arbitrary non-empty subset of S. This paper studies the K-separation properties of Rees factors and amalgamated coproducts, gives the characterizations of K-separation property by pullback diagrams, and discusses the homological classification problem of K-separation property on free(projective, principally weakly flat)Rees factor S-acts.

Key words: K-separation, principally weak flatness, torsion free

中图分类号:

O152.7

王雅婷,乔虎生. K-分离性质对幺半群的刻画[J]. 《山东大学学报(理学版)》, 2022, 57(6): 31-35.

WANG Ya-ting, QIAO Hu-sheng. Characterizations of monoids by K-separation property[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(6): 31-35.

参考文献

[1] 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.
[2] 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.
[3] BULMAN-FLEMING S. Flat and strongly flat S-systems[J]. Communications in Algebra, 1992, 20(9):2553-2567.
[4] KHANJANZADEH Z, MADANSHEKAF A. Weak ideal topology in the topos of right acts over a monoid[J]. Communications in Algebra, 2018, 46(5):1868-1888.
[5] 乔虎生, 石学勤. 弱挠自由Rees商序S-系的同调分类[J]. 山东大学学报(理学版), 2018, 53(8):49-52. QIAO Husheng, SHI Xueqin. On homological classification of weakly torsion free Rees factor S-posets[J]. Journal of Shandong University(Natural Science), 2018, 53(8):49-52.
[6] LAAN V. When torsion free acts are principally weakly flat[J]. Semigroup Forum, 2000, 60(2):321-325.

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K-分离性质对幺半群的刻画

Characterizations of monoids by K-separation property

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