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.
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页码：3019 / 3030
页数：12
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