Generalized formal power series rings
type: Item
instance of: scholarly article
title: Generalized formal power series rings
zbMATH Open document ID: 0915.13014
author: Ali Benhissi
published in: Archiv der Mathematik
publication date: 1998-10-25T00:00:00Z
review text: Let \(R\) be a commutative ring with 1 and \((S,\leq)\) a strictly ordered commutative monoid. Then \(A=[[R^{S,\leq}]]\), the set of functions \(f:S\to R\) such that \(\text{supp}(f)\) is artinian and narrow, is a ring with 1 under pointwise addition and convolution, called the ring of generalized power series. In this paper, the author studies the prime and maximal ideals of \(A\) and completely determines the maximal ideals when \(s\geq 0\) for each \(s\in S\). He determines necessary and sufficient conditions for an \(f\in A\) to be nilpotent when \(\text{char} R\) is nonzero and \(S\) is torsion-free. He also determines some sufficient conditions for \(A\) to be integrally closed when \(R\) is an integral domain and \(S\) is torsion-free and completely integrally closed.
reviewed by: David F. Anderson
Mathematics Subject Classification ID: 13F25
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13B22
zbMATH DE Number: 1185640
zbMATH Keywords: prime ideals
zbMATH Keywords: integral closure
zbMATH Keywords: ring of generalized power series
zbMATH Keywords: maximal ideals
MaRDI profile type: Publication
full work available at URL: s000130050196
OpenAlex ID: W2085617923
DOI: 10.1007/S000130050196
description: scientific article; zbMATH DE number 1185640