Taiwanese Journal of Mathematics

Skew Generalized Power Series Rings and the McCoy Property

Masoome Zahiri, Rasul Mohammadi, Abdollah Alhevaz, and Ebrahim Hashemi

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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.

Article information

Taiwanese J. Math., Volume 23, Number 1 (2019), 63-85.

Received: 7 January 2018
Revised: 1 July 2018
Accepted: 6 August 2018
First available in Project Euclid: 13 August 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16S35: Twisted and skew group rings, crossed products
Secondary: 16N40: Nil and nilpotent radicals, sets, ideals, rings 06F05: Ordered semigroups and monoids [See also 20Mxx]

skew generalized power series ring $(S,\omega)$-McCoy ring strictly ordered monoid unique product monoid reversible ring semi-regular ring


Zahiri, Masoome; Mohammadi, Rasul; Alhevaz, Abdollah; Hashemi, Ebrahim. Skew Generalized Power Series Rings and the McCoy Property. Taiwanese J. Math. 23 (2019), no. 1, 63--85. doi:10.11650/tjm/180805. https://projecteuclid.org/euclid.twjm/1534125615

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