| This thesis discusses the necessary and sufficient conditions that a sum of two semimodules is a direct sum.Then it gives the dimensional formula of two semimodules over a commutative semiring.After that,it introduces the definition of a standard basis of a semimodule,and obtains the condition that a set of vectors is a standard basis by comparing the standard basis with a free basis.Finally,this thesis shows some properties of a standard basis. |
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