Extension of free sets over commutative semirings

被引：1

作者：

Shu, Qian-yu ^{[1
]}

Wang, Xue-ping ^{[2
]}

Qiao, Lei ^{[2
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing, Jiangsu, Peoples R China

[2] Sichuan Normal Univ, Sch Math Sci, Chengdu 610066, Sichuan, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2021年 / 69卷 / 16期

基金：

中国博士后科学基金; 中国国家自然科学基金;

关键词：

Commutative semiring; semimodule; free set; free basis; LINEAR INDEPENDENCE; SEMILINEAR SPACES; BASES; MATRICES;

D O I：

10.1080/03081087.2019.1704209

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with extensions of free sets over commutative semirings. First, we discuss a necessary and sufficient condition that a finitely generated -semimodule is free, and by the way, we give a necessary and sufficient condition that a finite set in a finitely generated -semimodule is free. We then use these necessary and sufficient conditions to investigate the conditions that a free set in a finitely generated -semimodule can be extended to a free basis.

引用

页码：3019 / 3030

页数：12

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