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2020•LIBERTAS MATHEMATICA (new series)Requires access

A CLASS OF 2-STABLE COMMUTATIVE SEMIRINGS

Amir M. Rahimi

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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 nite 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.

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What this paper is about

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 nite 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.

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Available 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 nite 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.

Key concepts: Semiring, Mathematics, Class (philosophy), Commutative property, Combinatorics, Stability (learning theory), Natural number, Kleene algebra

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