Modules over discrete valuation rings
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.''
realization of rings as endomorphism rings
indecomposable torsion-free modules of finite rank
modules determined by their endomorphism algebra
scientific article; zbMATH DE number 6944286
scientific article