关于S系的覆盖

doi:10.6040／j.issn.1671.9352.0.2016.037

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (10): 22-27.doi: 10.6040／j.issn.1671.9352.0.2016.037

关于S系的覆盖

李焕云,乔虎生

西北师范大学数学与统计学院, 甘肃兰州 730070

出版日期:2016-10-20 发布日期:2016-10-17
通讯作者: 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
作者简介:李焕云(1989— ), 女, 硕士研究生, 研究方向为半群代数理论. Email:1639972670@qq.com
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 covers of S acts

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

Online:2016-10-20 Published:2016-10-17

摘要/Abstract

摘要： 设S是幺半群, FGWI, WPF, STF分别表示有限生成弱内射右S系、弱拉回平坦右S系和强挠自由右S系的类。证明了在有左零元的左reversible幺半群上,每一个右S系Ai∈FGWI当且仅当∪[DD(-*3]·[DD)]i∈IAi∈FGWI;在Noetherian幺半群上,任意fg弱内射S系的有向上极限是fg弱内射的;同时考虑了WPF覆盖和STF覆盖,给出了每一个右S系都有FGWI覆盖的条件。证明了若S是有有限几何型的有限生成幺半群,每一个右S系都有WPF覆盖,以及在任意幺半群S上,每一个右S系都有STF覆盖。

关键词: 有向上极限, WPF覆盖, STF覆盖, 余积, FGWI覆盖

Abstract: Let S be a monoid, FGWI, WPF and STF denote the class of finitely generated weakly injective right S acts, weakly pullback flat right S acts and strongly torsion free right Sacts respectively. It is proved that if S is a left reversible monoid with a left zero, then every rightS actAi∈FGWI if and only if the coproduct ∪[DD(-*3]·[DD)]i∈IAi∈FGWI. IfS is a Noetherian monoid, then the directed colimit of fgweakly injective Sacts is fgweakly injective. At the same time, WPF covers and STF covers are investigated, the condition over which every right Sact has a FGWI cover is obtained. It is proved that every right Sact has a WPF cover over a finitely generated monoid with a finite geometric type and every right Sact has a STFcover over any monoid S.

李焕云,乔虎生. 关于S系的覆盖[J]. 山东大学学报（理学版）, 2016, 51(10): 22-27.

LI Huan-yun, QIAO Hu-sheng. On covers of S acts[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(10): 22-27.

参考文献

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关于S系的覆盖

On covers of S acts

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