The further study of semimodules over commutative semirings

摘要

In this paper, we investigate the bases and dimension in finitely generated subsemimodules over commutative semirings. First, we give a sufficient condition for each basis of generated subsemimodule W to have the same number of elements. Particularly, in a cancellative and yoked semiring we show that the dimension of W is well-defined, and there exists a subsemimodule W such that Then we present a series of related properties of free sets in a free generated subsemimodule. Finally, we mainly study some properties of range and kernel of linear transformation for semimodules M, discuss the construction of range and kernel in detail, and present some conditions that the formula in classical linear algebra holds.