A class of commutative semirings with stable range 2. Issue 8 (17th November 2018)

• Record Type: Journal Article
• Authors: Rahimi, Amir M.
• Is Part Of: Quaestiones mathematicae. Volume 41:Issue 8(2018)
• Page Start: 1061
• Page End: 1071
• Publication Date: 2018-11-17
• Subjects: 16Y60; B- and BJ-semirings -- stable range of a commutative semiring -- subtractive ideal (= k-ideal) -- simple semiring -- Gelfand semiring; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2017.1419389
• Languages: English
• ISSNs: 1607-3606

Abstract

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.