A class of commutative semirings with stable range 2

Abstract

The notion and some properties of B-rings, in a natural way, are extended to B- and B_J -semirings which is somewhat similar to the notion of rings having stable range 2. Besides some examples and other results, it is shown that a Gelfand semiring [in particular, a simple semiring] has stable range one and is also a B-semiring (consequently, a B_J -semiring). Finally, we study a class of B_J -semirings and as a counterexample to the case of finite rings, construct two finite semirings such that neither of them is a B_J -semiring.