Polynomial extensions of semistar operations
type: Item
instance of: scholarly article
title: Polynomial extensions of semistar operations
zbMATH Open document ID: 1286.13004
author: Gyu Whan Chang
author: Marco Fontana
author: Mi Hee Park
published in: Journal of Algebra
publication date: 2014-03-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1306.3650
review text: Let \(D\) be an integral domain. The paper under review is devoted to the following problem: how to extend ``in a canonical way'' an arbitrary semistar operation of \(D\) to the polynomial ring \(D[X]\). The first attempts were done by \textit{G. Picozza} [Houston J. Math. 33, No. 2, 415--432 (2007; Zbl 1114.13006)] and then by the first two authors of this paper [J. Algebra 318, No. 1, 484--493 (2007; Zbl 1136.13011) and Commun. Algebra 39, No. 6, 1956--1978 (2011; Zbl 1234.13011)]. Their study is focused on the stable semistar operations of finite type. In this paper, the authors provide a complete solution to this problem in the most general setting. As an application, they show that, in the particular cases of stable semistar operations of finite type or semistar operations defined by families of over-rings.
reviewed by: Siamak Yassemi
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13A18
zbMATH DE Number: 6266632
zbMATH Keywords: semistar operation
zbMATH Keywords: finite type
zbMATH Keywords: stable
zbMATH Keywords: strict extension
zbMATH Keywords: \(d\)-, \(b\)-, \(v\)-, \(t\)-, \(w\)-operation
MaRDI profile type: Publication
OpenAlex ID: W1979177616
Wikidata QID: Q112881553
arXiv ID: 1306.3650
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DOI: 10.1016/J.JALGEBRA.2013.05.020
description: scientific article