Modules over discrete valuation rings
type: Item
instance of: scholarly article
title: Modules over discrete valuation rings
zbMATH Open document ID: 1404.13002
DOI: 10.1515/9783110611144
author: P. A. Krylov
author: A. A. Tuganbaev
published in: De Gruyter Expositions in Mathematics
publication date: 2018-09-26T00:00:00Z
review text: As it is written in its introduction, ``This book is the second, updated and supplemented, edition of the book `Modules over Discrete Valuation Domains' of the same authors [Berlin: Walter de Gruyter (2008; Zbl 1144.13001)] Compared with the first edition, a small chapter 9 `Appendix' (Sections 9.1--9.3) was added, the bibliography was expanded, and minor corrections were made.'' So, for a presentation of this second edition and its first eight chapters, we can refer to the review of the first edition by Gábor Braun, Zbl 1144.13001. For a presentation of Chapter 9, we cite its introduction: ``Chapter 9 covers the following topics: {\parindent=6mm \begin{itemize}\item[-] isomorphic automorphism groups of \(p\)-adic torsion-free modules (Section 9.1), \item[-] isomorphism theorems for radicals (Section 9.2), \item[-] miscellaneous results (Section 9.3).'' \end{itemize}} Moreover, ``All sections contain exercises beginning with Section 1.2. Some exercises contain results of various papers. We present 34 open problems which seem to be interesting''. At the end of each chapter there are some historical remarks. As the authors, I think ``that this book is useful to young researchers as well as experienced specialists.''
Mathematics Subject Classification ID: 13-02
Mathematics Subject Classification ID: 13F30
Mathematics Subject Classification ID: 13C05
zbMATH DE Number: 6944286
zbMATH Keywords: modules over discrete valuation domains
zbMATH Keywords: basic submodule
zbMATH Keywords: Harrison-Matlis equivalence
zbMATH Keywords: realization of rings as endomorphism rings
zbMATH Keywords: indecomposable torsion-free modules of finite rank
zbMATH Keywords: Warfield modules
zbMATH Keywords: modules determined by their endomorphism algebra
zbMATH Keywords: Kaplansky method
zbMATH Keywords: transitive modules
zbMATH Keywords: fully transitive modules
reviewed by: Francois Couchot
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1515/9783110611144
OpenAlex ID: W2893930220
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description: scientific article; zbMATH DE number 6944286