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2011 PF-rings of skew generalized power series
Amit Bhooshan Singh
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Tbilisi Math. J. 4: 39-44 (2011). DOI: 10.32513/tbilisi/1528768867

Abstract

Let $R$ be a ring which is $S$-compatible and $(S,\omega)$-Armendariz. In this paper, we investigate that the skew generalized power series ring $R[[S,\omega]]$ is a PF-ring if and only if for any two $S$-indexed subsets $P$ and $Q$ of $R$ such that $Q \subseteq ann_R (P)$ and there exists $a\in ann_R (P)$ such that $q a=q$ for all $q \in Q$. Further, we prove that if $R$ be a Noetherian ring then $R[[S,\omega]]$ is a PP-ring if and only if $R$ is a PP-ring.

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Amit Bhooshan Singh. "PF-rings of skew generalized power series." Tbilisi Math. J. 4 39 - 44, 2011. https://doi.org/10.32513/tbilisi/1528768867

Information

Received: 29 March 2011; Revised: 20 September 2011; Accepted: 4 November 2011; Published: 2011
First available in Project Euclid: 12 June 2018

zbMATH: 1278.13026
MathSciNet: MR2886757
Digital Object Identifier: 10.32513/tbilisi/1528768867

Subjects:
Primary: 13F25
Secondary: 13C11

Rights: Copyright © 2011 Tbilisi Centre for Mathematical Sciences

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Vol.4 • 2011
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