Armendariz Semirings and Semicommutative Semirings

Dharitri Sinha; Md Salim Masud Molla

Dharitri Sinha University of Calcutta
Md Salim Masud Molla

Keywords: Armendariz semiring, p.s Armendariz semiring, Abelian semir- ing, Reduced semiring, Right quotient semiring, Semicommutative semiring, k-ideal.

Abstract

In this paper we study Armendariz semiring, which has been introduced by V.Gupta and P.kumar, in the paper entitled `Armendariz and qusi-Armendariz and PS-semirings' [8]. We extend some results of Armendariz rings and semi-commutative rings of [3] for semirings with $1\neq0$. (i)We obtain that for a semirings S, S is Armendariz if and only eS and (1+e)S are Armendariz for every idempotent e of S if and only if eS and (1+e)S are Armendariz for every central idempotent e of S. (ii) For a semiring S if S/I is an Armendariz semiring for some reduced ideal I of S then S is Armendariz.

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References

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