A class of commutative semirings with stable range 2. Issue 8 (17th November 2018) - Rahimi, Amir M.
Abstract: The notion and some properties of B -rings, in a natural way, are extended to B - and BJ -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 BJ -semiring). Finally, we study a class of BJ -semirings and as a counterexample to the case of finite rings, construct two finite semirings such that neither of them is a BJ -semiring.