%0 Journal Article
%T 交换半环上半线性空间的维数<br>Dimensions of semilinear spaces over commutative semirings
%A 张后俊
%A 储茂权&lt
%A br&gt
%A ZHANG Hou-jun
%A CHU Mao-quan
%J 山东大学学报（理学版）
%D 2015
%R 10.6040/j.issn.1671-9352.0.2014.229
%X 摘要： 探究了交换半环上半线性空间的维数。给出了交换半环L上半线性空间Vn维数为n的充要条件且得到了Vn与V1之间的关系。此外介绍了半线性空间中半线性变换A及其值域A(V)与核A-1(0)的概念, 并证明了等式 dim(A(Vn))+dim(A-1(0))=dim(Vn)。<br>Abstract: The dimensions of semilinear spaces over commutative semirings L are investigated. Some necessary and sufficient conditions that dim(Vn)=n are given, and the relationship between Vn and V1 are obtained, where Vn and V1 are finite dimensional semilinear spaces over L. Moreover, the concepts of semilinear transformation A, and the range A(Vn) and nuclear A-1(0) of A are introduced and the equation dim(A(Vn))+dim(A-1(0))=dim(Vn) is proved
%K 维数
%K 半线性变换
%K 交换半环
%K 半线性空间
%K &lt
%K br&gt
%K commutative semiring
%K semilinear spaces
%K dimensions
%K semilinear transformation
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2014.229