Paykan, Kamal; Moussavi, Ahmad McCoy property and nilpotent elements of skew generalized power series rings. (English) Zbl 1383.16037 J. Algebra Appl. 16, No. 10, Article ID 1750183, 33 p. (2017). Summary: Let \(R\) be a ring, \((S,\leq)\) a strictly ordered monoid and \(\omega:S \to \mathrm{End}(R)\) a monoid homomorphism. The skew generalized power series ring \(R[[S,\omega]]\) is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal’cev-Neumann Laurent series rings. In this paper, we consider the problem of determining when \(f \in R[[S,\omega]]\) is nilpotent in \(R[[S,\omega]]\). We study various annihilator properties and a variety of conditions and related properties that the skew generalized power series \(R[[S,\omega]]\) inherits from \(R\). We also introduce and study the \((S,\omega)\)-McCoy condition on \(R\), a generalization of the standard McCoy condition from polynomials to skew generalized power series. We resolve the structure of \((S,\omega)\)-McCoy rings and obtain various necessary or sufficient conditions for a ring to be \((S,\omega)\)-McCoy. As particular cases of our general results we obtain several new theorems on the McCoy condition. Moreover various examples of \((S,\omega)\)-McCoy rings are provided. Cited in 6 Documents MSC: 16U80 Generalizations of commutativity (associative rings and algebras) 16S36 Ordinary and skew polynomial rings and semigroup rings 16N40 Nil and nilpotent radicals, sets, ideals, associative rings Keywords:skew generalized power series ring; \((S,\omega)\)-McCoy ring; \((S,\omega)\)-Armendariz ring; (weak) zip ring; semicommutative ring; skew triangular matrix ring PDFBibTeX XMLCite \textit{K. Paykan} and \textit{A. Moussavi}, J. 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