Hom-Leibniz-Rinehart代数的交叉模  

Crossed Modules of Hom-Leibniz-Rinehart Algebras

作　　者：毕艳会[1] 陈丹露 张明同 BI Yan-hui;CHEN Dan-lu;ZHANG Ming-tong(School of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China;Shandong Shouguang Educational Science Research Center,Shandong Weifang 262700,China)

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063 [2]山东省寿光市教育科学研究中心,山东潍坊262700

出　　处：《南昌航空大学学报（自然科学版）》2022年第1期28-32,共5页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(1196010189,11601219)。

摘　　要：在前人研究的基础上,对Hom-非交换代数做了进一步研究。首先,给出了关于Hom-Leibniz-Rinehart代数上Hom-作用的定义。其次,在Hom-Leibniz-Rinehart代数和Hom-Leibniz A-代数的直和代数上定义了左锚映射、右锚映射和自同态,使二者构成半直积结构,证明了其Hom-作用与Hom-Leibniz-Rinehart代数之间存在一一对应的关系。最后,给出了Hom-Leibniz-Rinehart代数交叉模的定义,证明了其交叉模与代数同态之间的等价关系。On the basis of previous studies,Hom-noncommutative algebra is further studied.Firstly,the definition of Hom-action on Hom-Leibniz-Rinehart algebra is given.Secondly,on the directsum of Hom-Leibniz-Rinehart algebras and Hom-Leibniz A-algebras,it is defined that the left anchor,right anchor and endomorphism are semi-direct products,and it is proved that there is a one-to-one correspondence between their actions and Hom-Leibniz-Rinehart-algebras.Finally,the cross module of Hom-Leibniz-Rinehart algebra is defined,and the corresponding relationship between cross module and algebraic homomorphism is proved.

关 键 词：Hom-Leibniz-Rinehart代数 Hom-作用 交叉模 

分 类 号：O154.2[理学—数学]