Warfield domains: module theory from linear algebra to commutative algebra through abelian groups
type: Item
instance of: scholarly article
title: Warfield domains: module theory from linear algebra to commutative algebra through abelian groups
zbMATH Open document ID: 1054.13005
published in: Milan Journal of Mathematics
publication date: 2004-09-07T00:00:00Z
review text: In this well-written survey, the author has three main goals. The first goal is to outline the chronological development of the theory of reflexive and related domains from the sixties to the present days. The second goal is to illustrate the various characterizations of Warfield domains: the non-intrinsic ones through the reflexivity of their overrings, and the intrinsic ones in the classical cases of Noetherian and integrally closed domains, and in the general case. The third goal is to present a series of results on the good behaviour of the torsionless modules of finite rank over Warfield domains with respect to direct sum decompositions. This subject goes back to a pioneering theorem in Steinitz's 1912 paper [cf. \textit{E. Steinitz}, Math. Ann. 72, 297--345 (1912; JFM 43.0274.01)].
reviewed by: Siamak Yassemi
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 13-03
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 01A61
zbMATH DE Number: 2099224
zbMATH Keywords: Warfield domains
zbMATH Keywords: torsionless domains
zbMATH Keywords: reflexive domains
zbMATH Keywords: direct sum decomposition
author: Luigi Salce
MaRDI profile type: Publication
full work available at URL: s00032-002-0005-7
OpenAlex ID: W2088741995
DOI: 10.1007/S00032-002-0005-7
description: scientific article; zbMATH DE number 2099224