# 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.

The Library of Congress (USA) reference page : http://lccn.loc.gov/cn2013300046.

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skew polynomials1.tex

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