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## Bases of a free semimodule are small

Linear Algebra and its Applications. 2015. Vol. 466. P. 38-40.

A generating set G of a left semimodule S over a semiring R is called a basis if no proper subset of G generates S. We prove that Rn$has no basis of cardinality exceeding$qn, where q is the largest cardinality of bases of R.