Special properties of generalized power series
type: Item
instance of: scholarly article
title: Special properties of generalized power series
zbMATH Open document ID: 0852.13008
published in: Journal of Algebra
publication date: 1996-12-12T00:00:00Z
review text: Given a commutative ring \(R\) and a strictly ordered monoid \((S, \leq)\), the generalized power series ring \(A = RS, \leq\) is defined to be the set of all maps \(f : S \to R\) such that support\((f) = \{s \in S : f(s) \neq 0\}\) is artinian and narrow. The addition and multiplication on \(A\) are defined appropriately. -- The purpose of this paper is to investigate the validity of various results about power series rings in the case of generalized power series rings. One of the many interesting results in this paper is that: If \((S, \leq)\) is artinian and narrow as an ordered set and if \(S\) is a free monoid then for a field \(R\), the generalized power series ring \(A = RS, \leq\) is an UFD. There are many other results of similar nature. Of particular interest among them are the results on seminormality.
reviewed by: Satyagopal Mandal
Mathematics Subject Classification ID: 13F25
zbMATH DE Number: 763961
zbMATH Keywords: generalized power series ring
zbMATH Keywords: free monoid
author: Paulo Ribenboim
MaRDI profile type: Publication
full work available at URL: jabr.1995.1103
OpenAlex ID: W1996713275
DOI: 10.1006/JABR.1995.1103
description: scientific article; zbMATH DE number 763961