交换半环上半线性空间的线性变换  

Linear Transformations of Semilinear Spaces over Commutative Semirings

作　　者：张兴均 吴莉 王学平 ZHANG Xingjun;WU Li;WANG Xueping(College of Mathematical Science,Sichuan Normal University,Chengdu 610066,Sichuan;College of Mathematics and Computer Science,Aba Teachers College,Wenchuan 623002,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066 [2]阿坝师范学院数学与计算机科学学院,四川汶川623002

出　　处：《四川师范大学学报（自然科学版）》2020年第2期181-186,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(61573240)。

摘　　要：介绍半线性空间上线性变换、幂等变换、可逆变换的概念,定义线性变换的运算,讨论幂等变换、可逆变换的一些基本性质,并得到线性变换的值域与核的一些关系.特别地,证明在单变换下,值域的基的原像构成半线性空间的基.This paper mainly introduces the concepts of a linear transformation,an idempotent transformation and an invertible transformation,and defines the operations of transformations in semilinear spaces over commutative semirings.It then discusses some properties of the idempotent transformations and the invertible transformations,respectively.Some relationships between images and kernels of the linear transformation are showed.In particular,it proves that the inverses of vectors of a basis in images form a basis of a semilinear space under the condition that the linear transformation is injective.

关 键 词：半环 半线性空间 线性变换 线性变换的值域 线性变换的核 

分 类 号：O159[理学—数学] O151.2[理学—基础数学]