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On a ring property generalizing power-Armendariz and central Armendariz rings. (English) Zbl 1433.16021
Summary: We in this note consider a class of rings which is related to both power-Armendariz and central Armendariz rings, in the spirit of Armendariz and Kaplansky. We introduce central power-Armendariz as a generalization of them, and study the structure of central products of coefficients of zero-dividing polynomials. We also observe various sorts of examples to illuminate the relations between central power-Armendariz and related ring properties.
MSC:
16N40 Nil and nilpotent radicals, sets, ideals, associative rings
16S36 Ordinary and skew polynomial rings and semigroup rings
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