Bases in semilinear spaces over zerosumfree semirings
Bases in semilinear spaces over zerosumfree semirings
复制标题
DOI：
10.1016/j.laa.2011.04.024
复制
发表时间：
2011-12
影响因子：
1.1
通讯作者：
Q. Shu;Xue-ping Wang
中科院分区：
文献类型：
--
作者：
Q. Shu;Xue-ping Wang
This paper investigates the cardinality of a basis and the characterizations of a basis in semilinear space of n-dimensional vectors over zerosumfree semirings. First, it discusses the cardinality of a basis and gives some necessary and sufficient conditions that each basis has the same number of elements. Then it presents some conditions that a set of vectors is a basis and that a set of linearly independent vectors can be extended to a basis. In the end, it shows a necessary and sufficient condition that two semilinear spaces are isomorphic.
