부산대학교 도서관

Summary: ``The dimensions of semilinear spaces over commutative semirings $L$ are investigated. Some necessary and sufficient conditions that $\dim(V_n)=n$ are given, and the relationship between $V_n$ and $V_1$ are obtained, where $V_n$ and $V_1$ are finite dimensional semilinear spaces over $L$. Moreover, the concepts of semilinear transformation $\Cal A$, and the range $\Cal A(V_n)$ and nuclear $\Cal A^{-1}({\bf 0})$ of $\Cal A$ are introduced and the equation $\dim(\Cal A(V_n))+\dim(\Cal A^{-1}({\bf 0}))=\dim(V_n)$ is proved.''