European Academic Research ISSN 2286-4822
ISSN-L 2286-4822
Impact Factor: 3.4546 (UIF)
DRJI Value : 5.9 (B+)
Article Details :
Article Name :
On Linearly S-Quasi-Armendariz Rings
Author Name :
ELTIYEB ALI, AYOUB ELSHOKRY
Publisher :
Bridge Center
Article URL :
Abstract :
Let R be a ring, (S,?) a strictly ordered monoid. Properties of the ring ?? ?? S,? R of generalized power series with coefficients in R and exponents in S are considered in this paper. We devoted to introduce and study linearly S -quasiArmendariz ring, which is unify the notions of linearly S - Armendariz ring and S-quasi-Armendariz ring. It is shown that, if R is linearly S -quasi-Armendariz ring, U is a nonempty subset in R is a two-sided ideal of R , A l (U) ? R for all s ? S , then A R is linearly S -quasi-Armendariz. Also, we prove that, R is semiprime if and only if R is reduced linearly S - quasi-Armendariz. Moreover, a necessary and sufficient conditions are given for rings under which the classical left ring of quotients of R , is linearly S -quasi-Armendariz.
Keywords :
generalized power series ring, linearly S -quasiArmendariz ring, semicommutative ring.

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