交换半环上半模的标准基  

Standard Bases in Semimodules over Commutative Semirings

作　　者：周艺璇 王学平 ZHOU Yixuan;WANG Xueping(Department of Sciences and Engineering,Sichuan Minzu College,Kangding 626001,Sichuan;School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川民族学院理工学院,四川康定626001 [2]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2021年第2期156-162,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(12071325)。

摘　　要：首先讨论交换半环上半模的生成集成为自由基的充要条件,以及子半模的和是直和的充要条件并给出维数公式.然后提出标准基的概念,将标准基与自由基作对比,讨论向量组是标准基的条件.最后讨论标准基的基本性质.This paper discusses the necessary and sufficient conditions that a generating set of a semimodule is a free basis,and a sum of two semimodules is a direct sum,separately,and gives the dimensional formula of two semimodules over a commutative semiring.Then it introduces the definition of a standard basis of a semimodule,and obtains the condition that a set of vectors is a standard basis by comparing the standard basis with a free basis.Finally,it shows some properties of the standard basis.

关 键 词：半模 自由基 标准基 

分 类 号：O153[理学—基础数学]