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A CLASS OF 2-STABLE COMMUTATIVE SEMIRINGS
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.
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.
Keywords
(Strongly) B- and (Strongly) BJ -semirings; S-relative B- and S-relative BJ - semirings; subtractive ideal (= k-ideal); simple semiring; Gelfand semiring; polynomial semiring; stable range of a commutative semiring.
DOI: http://dx.doi.org/10.14510%2Flm-ns.v39i2.1428