Extensions of Rings and Modules

by Gary F. Birkenmeier, Jae Keol Park, S Tariq Rizvi

Overview

The "extensions" of rings and modules have yet to be explored in detail in a research monograph. This book presents state of the art research and also stimulating new and further research. Broken into three parts, Part I begins with basic notions, terminology, definitions and a description of the classes of rings and modules. Part II considers the transference of conditions between a base ring or module and its extensions. And Part III utilizes the concept of a minimal essental extension with respect to a specific class (a hull).

Mathematical interdisciplinary applications appear throughout. Major applications of the ring and module theory to Functional Analysis, especially C*-algebras, appear in Part III, make this book of interest to Algebra and Functional Analysis researchers. Notes and exercises at the end of every chapter, and open problems at the end of all three parts, lend this as an ideal textbook for graduate or advanced undergradate students.

Product Details

ISBN-13:	9781489997142
Publisher:	Springer New York
Publication date:	08/08/2015
Edition description:	Softcover reprint of the original 1st ed. 2013
Pages:	432
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Preliminaries and Basic Results.- Injectivity and Some of Its Generalizations.- Baer, Rickart, and Quasi-Baer Rings.- Baer, Quasi-Baer Modules, and Their Applications.- Triangular Matrix Representations and Triangular Matrix Extensions.- Matrix, Polynomial, and Group Ring Extensions.- Essential Overring Extensions - Beyond the Maximal Ring of Quotients.- Ring and Module Hulls.- Hulls of Ring Extensions.- Applications to Rings of Quotients and C* Algebras.- Open Problems and Questions.- References.- Index.

Editorial Reviews

The authors of this monograph have made important contributions to this subject during the last few decades and they aim to give a comprehensive treatment of the topic. … Each chapter is followed by brief historical notes. There is a large number of exercises and a bibliography with over 400 entries. This volume fills a gap in the literature and will be an important reference for ring theorists in years to come.” (C. Baxa, Monatshefte für Mathematik, Vol. 180, 2016)

“This book is to present the state of the art on the subject, which includes some of the most recent work done on these topics. … The monograph is as self-contained as possible, with extensive references that are useful for further study. The book is very well written and it can serve as a good tool for graduate students, ting theorists and researchers in algebra and analysis.” (J. Jirásko, Mathematical Reviews, September, 2014)

“This book is a research monograph intended for research mathematicians and advanced graduate students in ring theory. … the book is well-organized, well-written and informative. It will be a handy companion for ring theorists in general, but an essential tool for researchers who want to extend our knowledge of extensions, hulls and the transfer of properties between rings and modules and their extensions.” (Stefan Veldsman, zbMATH, Vol. 1291, 2014)

From the Publisher