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IJMSI 2024, 19(2): 77-93 |
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Mehdi-Nezhad E, Rahimi A M. A Class of Commutative Semirings with Stable Range 2 II. IJMSI 2024; 19 (2) :77-93
URL: http://ijmsi.ir/article-1-1770-en.html
URL: http://ijmsi.ir/article-1-1770-en.html
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.
Keywords: (Strongly) B- and (Strongly) B_J-semirings, S-relative B- and Srelative B_J-semirings, Subtractive ideal (= k-ideal), Simple semiring, Gelfand semiring, Polynomial semiring, Stable range of a commutative semiring.
Type of Study: Research paper |
Subject:
Special
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