Invariance of Modules under Automorphisms of their Envelopes and Covers

Ashish K. Srivastava (St Louis University, Missouri), Askar Tuganbaev, Pedro A. Guil Asensio (Universidad de Murcia, Spain)

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English

Cambridge University Press
18 March 2021

Mathematics; Algebra

Series: London Mathematical Society Lecture Note Series

The theory of invariance of modules under automorphisms of their envelopes and covers has opened up a whole new direction in the study of module theory. It offers a new perspective on generalizations of injective, pure-injective and flat-cotorsion modules beyond relaxing conditions on liftings of homomorphisms. This has set off a flurry of work in the area, with hundreds of papers using the theory appearing in the last decade. This book gives the first unified treatment of the topic. The authors are real experts in the area, having played a major part in the breakthrough of this new theory and its subsequent applications. The first chapter introduces the basics of ring and module theory needed for the following sections, making it self-contained and suitable for graduate students. The authors go on to develop and explain their tools, enabling researchers to employ them, extend and simplify known results in the literature and to solve longstanding problems in module theory, many of which are discussed at the end of the book.

By: Ashish K. Srivastava (St Louis University Missouri), Askar Tuganbaev, Pedro A. Guil Asensio (Universidad de Murcia, Spain)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 228mm, Width: 152mm, Spine: 13mm
Weight: 350g
ISBN: 9781108949538
ISBN 10: 1108949533
Series: London Mathematical Society Lecture Note Series
Pages: 232
Publication Date: 18 March 2021
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

1. Preliminaries; 2. Modules invariant under automorphisms of envelopes; 3. Structure and properties of modules invariant under automorphisms; 4. Automorphism-invariant modules; 5. Modules coinvariant under automorphisms of their covers; 6. Schröder–Bernstein problem; 7. Automorphism-extendable modules; 8. Automorphism-liftable modules; 9. Open problems; References; Index.

Ashish K. Srivastava is Professor of Mathematics at Saint Louis University. He has published more than 40 research papers and co-authored the monograph Cyclic Modules and the Structure of Rings (2012). Askar Tuganbaev is Professor at the National Research University 'Moscow Power Engineering Institute' and Lomonosov Moscow State University. He is the author of 10 monographs, including Arithmetical Rings and Endomorphisms (2019), Rings Close to Regular (2002) and Laurent Series Rings and Related Rings (2020). Pedro A. Guil Asensio is Assistant Professor at the University of Murcia in Spain. He has published more than 60 research papers in noncommutative algebra.

Reviews for Invariance of Modules under Automorphisms of their Envelopes and Covers

'This monograph covers many interesting and important results on these topics that have appeared in recent years.' Xiaoxiang Zhang, Mathematical Reviews/MathSciNet