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Standard bases in semimodules over commutative semirings. (Chinese. English summary) Zbl 1488.13069

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
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