J-Armendariz rings
Abstract
We introduce the notion of J-Armendariz rings, which are
a generalization of weak Armendariz rings and investigate their proper-
ties. We show that local rings are J-Armendariz. Also, we prove that a
ring R is J-Armendariz if and only if R[[x]] is J-Armendariz. It is shown
that the J-Armendariz property is not Morita invariant. As a specic
case, we show that the class of J-Armendariz rings lies properly between
the class of one-sided quasi-duo rings and the class of perspective rings.
a generalization of weak Armendariz rings and investigate their proper-
ties. We show that local rings are J-Armendariz. Also, we prove that a
ring R is J-Armendariz if and only if R[[x]] is J-Armendariz. It is shown
that the J-Armendariz property is not Morita invariant. As a specic
case, we show that the class of J-Armendariz rings lies properly between
the class of one-sided quasi-duo rings and the class of perspective rings.
Keywords
Armendariz ring, Weak Armendariz ring, J-Armendariz ring, Perspective ring, Quasi duo-ring
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