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山东大学学报(理学版) ›› 2015, Vol. 50 ›› Issue (06): 45-52.doi: 10.6040/j.issn.1671-9352.0.2014.229

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交换半环上半线性空间的维数

张后俊, 储茂权   

  1. 安徽师范大学数学计算机科学学院, 安徽 芜湖 241003
  • 收稿日期:2014-05-20 修回日期:2014-11-05 出版日期:2015-06-20 发布日期:2015-07-31
  • 通讯作者: 储茂权(1958-),男,副教授,硕士生导师,研究方向为环模理论.E-mail:cmquan@mail.ahnu.edu.cn E-mail:cmquan@mail.ahnu.edu.cn
  • 作者简介:张后俊(1989-),男,硕士研究生,研究方向为环模理论.E-mail:1059378920@qq.com
  • 基金资助:
    国家自然科学基金资助项目(10971099)

Dimensions of semilinear spaces over commutative semirings

ZHANG Hou-jun, CHU Mao-quan   

  1. School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, Anhui, China
  • Received:2014-05-20 Revised:2014-11-05 Online:2015-06-20 Published:2015-07-31

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VnV1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)。

关键词: 维数, 半线性变换, 交换半环, 半线性空间

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.

Key words: commutative semiring, semilinear spaces, dimensions, semilinear transformation

中图分类号: 

  • O153.3
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