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February, 2019 Skew Generalized Power Series Rings and the McCoy Property
Masoome Zahiri, Rasul Mohammadi, Abdollah Alhevaz, Ebrahim Hashemi
Taiwanese J. Math. 23(1): 63-85 (February, 2019). DOI: 10.11650/tjm/180805


Given a ring $R$, a strictly totally ordered monoid $(S,\preceq)$ and a monoid homomorphism $\omega \colon S \to \operatorname{End}(R)$, one can construct the skew generalized power series ring $R[[S,\omega,\preceq]]$, consisting all of the functions from a monoid $S$ to a coefficient ring $R$ whose support is artinian and narrow, where the addition is pointwise, and the multiplication is given by convolution twisted by an action $\omega$ of the monoid $S$ on the ring $R$. In this paper, we consider the problem of determining some annihilator and zero-divisor properties of the skew generalized power series ring $R[[S,\omega,\preceq]]$ over an associative non-commutative ring $R$. Providing many examples, we investigate relations between McCoy property of skew generalized power series ring, namely $(S,\omega)$-McCoy property, and other standard ring-theoretic properties. We show that if $R$ is a local ring such that its Jacobson radical $J(R)$ is nilpotent, then $R$ is $(S,\omega)$-McCoy. Also if $R$ is a semicommutative semiregular ring such that $J(R)$ is nilpotent, then $R$ is $(S,\omega)$-McCoy ring.


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Masoome Zahiri. Rasul Mohammadi. Abdollah Alhevaz. Ebrahim Hashemi. "Skew Generalized Power Series Rings and the McCoy Property." Taiwanese J. Math. 23 (1) 63 - 85, February, 2019.


Received: 7 January 2018; Revised: 1 July 2018; Accepted: 6 August 2018; Published: February, 2019
First available in Project Euclid: 13 August 2018

zbMATH: 07021718
MathSciNet: MR3909990
Digital Object Identifier: 10.11650/tjm/180805

Primary: 16S35
Secondary: 06F05, ‎16N40

Rights: Copyright © 2019 The Mathematical Society of the Republic of China


Vol.23 • No. 1 • February, 2019
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