The Semirings with Invariant Basis Numbers

Abstract

In this paper, the semirings with invariant basis numbers are investigated. First, we give some properties of a semiring which has an invariant basis number, and then give some necessary and sufficient conditions that the direct sum of two semirings has an invariant basis number. As an application, we prove that division semirings, quasilocal semirings and stably finite semirings have invariant basis numbers, respectively.