交换半环上有限生成半模的基数问题  

The Cardinality Problem of Finite Generated Semimodules over Commutative Semirings

作　　者：张小梅 舒乾宇 ZHANG Xiaomei;SHU Qianyu(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]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5期592-600,共9页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(12071325)。

摘　　要：在交换半环中讨论强线性无关集和强线性无关基的一些问题.首先,在有限生成半模中讨论强线性无关集的一些性质以及它与自由集之间的关系.其次,讨论在有限生成半模中强线性无关基和半模GM-rank之间的关系.This paper investigates the property of a strongly linearly independent set and a strongly linearly independent basis of finite generated semimodules over commutative semirings.First it gives some characteristics of strongly linear independent sets and the relationship between free sets and strongly linearly independent sets of finite generated semimodules over commutative semirings.Then,it compares the relationship between cardinality of strongly linearly independent and GM-rank of finite generated semimodules.

关 键 词：交换半环 半模 基 强线性无关 GM-rank 

分 类 号：O153[理学—数学]