A Class of Commutative Semirings with Stable Range 2 II

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

The notion and some properties of (strongly) B-rings, in a natural way, are extended to (strongly) B- and (strongly) BJ-semirings which is somewhat similar to the notion of rings having stable range 2. Results are given showing the connection between several types of semirings whose finite sequences satisfy some stability condition, some involving the Jacobson k-radical of the semiring R. Besides some examples and other results, it is shown that R[x], the semiring of polynomials over a semiring R, is not a B-semiring (consequently, not a strongly B-semiring) when R is a zerosumfree semiring. We also study some algebraic properties of the S-relative B- and BJ-semirings with respect to a nonempty subset S of R.

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:19 Issue: 2, Nov 2024
Pages:
77 to 93
https://www.magiran.com/p2761610