Extensions of Rings and Modules

Gary F. Birkenmeier · Jae Keol Park · S Tariq Rizvi

jul. 2013 · Springer Science & Business Media

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The "extensions" of rings and modules has yet to be explored in detail in a research monograph. This book does that and much more, by presenting the state of the art research and also stimulating new and further research. The focus of this study of extensions includes the (quasi-) Baer property, the (quasi-) continuos property, the (FI-) extending property, and related concepts for rings and modules.

Starting in Part I with basic notions, terminology, definitions and a description of the classes of rings and modules satisfying the aforementioned conditions, this book is accessible to advanced students of mathematics. Part II considers the transference of these conditions between a base ring or module and its extensions. And Part III utilizes the concept of a minimal essential extension with respect to a specific class (a hull) to unify the subject.

Mathematical interdisciplinary applications appear throughout. Major applications of the ring and module theory to Functional Analysis, especially C*-algebras, appear in Part III, making 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 undergraduate students.