JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (06): 45-52.doi: 10.6040/j.issn.1671-9352.0.2014.229

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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

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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

CLC Number: 

  • O153.3
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