McCoy Rings Relative to a Monoid |
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Authors: | E. Hashemi |
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Affiliation: | 1. Department of Mathematics , Shahrood University of Technology , Shahrood, Iran eb_hashemi@yahoo.com |
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Abstract: | For a monoid M, we introduce M-McCoy rings, which are a generalization of McCoy rings and M-Armendariz rings; and investigate their properties. We first show that all reversible rings are right M-McCoy, where M is a u.p.-monoid. We also show that all right duo rings are right M-McCoy, where M is a strictly totally ordered monoid. Then we show that semicommutative rings and 2-primal rings do have a property close to the M-McCoy condition. Moreover, it is shown that a finitely generated Abelian group G is torsion free if and only if there exists a ring R such that R is G-McCoy. Consequently, several known results on right McCoy rings are extended to a general setting. |
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Keywords: | Armendariz rings M-Armendariz rings McCoy rings Semi-commutative rings |
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