The further study of semimodules over commutative semirings

Yuying Li, Xiaozhu Xu and Haifeng Zhang

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 20, 4929-4950

Abstract: 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 ℓ, we show that the dimension of W is well-defined, and there exists a subsemimodule W such that dimW>dimVn. 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 AM and kernel A−1{0} in detail, and present some conditions that the formula dimAM+dimA−1{0}=dim in classical linear algebra holds.

Date: 2020
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DOI: 10.1080/03610926.2019.1609516

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