Zhou, Yixuan; Wang, Xueping Standard bases in semimodules over commutative semirings. (Chinese. English summary) Zbl 1488.13069 J. Sichuan Norm. Univ., Nat. Sci. 44, No. 2, 156-162 (2021). Summary: This paper discusses the necessary and sufficient conditions under which a generating set of a semimodule is a free basis, and a sum of two semimodules is a direct sum, respectively, and gives the dimensional formula of two semimodules over a commutative semiring. Then it introduces the definition of a standard basis of a semimodule, and obtains the condition under which a set of vectors is a standard basis by comparing the standard basis with a free basis. Finally, some properties of the standard basis are shown. MSC: 13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 16Y60 Semirings Keywords:semimodules; free basis; standard basis PDFBibTeX XMLCite \textit{Y. Zhou} and \textit{X. Wang}, J. Sichuan Norm. Univ., Nat. Sci. 44, No. 2, 156--162 (2021; Zbl 1488.13069) Full Text: DOI