有弱局部单位半群的内射系  

Injective acts over semigroups with weak local units

作　　者：梁星亮[1,2] 乔彦赫 陈晓洁 Liang Xingliang;Qiao Yanhe;Chen Xiaojie(School of Mathematics and Data Science,Shaanxi University of Science and Technology,Xi'an 710021,China;School of Mathematics,Northwest University,Xi'an 710127,China;College of Art and Design,Shaanxi University of Science and Technology,Xi'an 710021,China)

机构地区：[1]陕西科技大学数学学院,陕西西安710021 [2]西北大学数学学院,陕西西安710127 [3]陕西科技大学设艺学院,陕西西安710021

出　　处：《纯粹数学与应用数学》2022年第4期547-556,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(12001345);省级大创项目(S202010708097);陕西省教育厅项目(18JK0087)。

摘　　要：将幺半群的同调分类理论与S-系理论有机结合,借助酉系范畴中的内射对象研究了有弱左局部单位半群的特征.利用函子与S-系同态的可收缩性给出内射S-系的等价刻画;通过S-系上方程组的容许性质,建立S-系的内射性与其方程组的可解性之间的联系;通过探索内射系与其基本扩张的关系,给出所有S-系是内射的有弱左局部单位半群的特征.This paper will combine homological classification of monoids with the theory of S-act, and characterize semigroups with common weak left local units by using injective S-acts in the category of unitary S-acts. By the Hom-functor and retraction of S-monomorphisms, some characterizations of injective S-acts are given. By the consistent property of systems of equations the relationship between injective S-acts and solvability of the system of equations is established. By exploring the relationship between essential extensions and injectivity, semigroups S with common weak left local units over which every left S-act is injective are characterized.

关 键 词：有弱左局部单位半群 S-系 内射性 基本扩张 

分 类 号：O152.7[理学—数学]