Mohamed Louzari. On skew polynomials over p.q.-baer and p.p.-modules

Natural Sciences / Mathematics / Algebra

Submitted on: Sep 11, 2012, 15:54:41

Description: Let $M_R$ be a module and $sigma$ an endomorphism of $R$. Let $min M$ and $ain R$, we say that $M_R$ satisfies the condition $mathcal{C}_1$ (respectively, $mathcal{C}_2$), if $ma=0$ implies $msigma(a)=0$ (respectively, $msigma(a)=0$ implies $ma=0$). We show that if $M_R$ is p.q.-Baer then so is $M[x;sigma]_{R[x;sigma]}$ whenever $M_R$ satisfies the condition $mathcal{C}_2$, and the converse holds when $M_R$ satisfies the condition $mathcal{C}_1$. Also, if $M_R$ satisfies $mathcal{C}_2$ and $sigma$-skew Armendariz, then $M_R$ is a p.p.-module if and only if $M[x;sigma]_{R[x;sigma]}$ is a p.p.-module if and only if $M[x,x^{-1};sigma]_{R[x,x^{-1};sigma]}$ ($sigmain Aut(R)$) is a p.p.-module. Many generalizations are obtained and more results are found when $M_R$ is a semicommutative module.

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