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The further study of semimodules over commutative semirings

Author

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  • Yuying Li
  • Xiaozhu Xu
  • Haifeng Zhang

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.

Suggested Citation

  • Yuying Li & Xiaozhu Xu & Haifeng Zhang, 2020. "The further study of semimodules over commutative semirings," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(20), pages 4929-4950, October.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:20:p:4929-4950
    DOI: 10.1080/03610926.2019.1609516
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