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Invariance of Modules under Automorphisms of their Envelopes and Covers


Part of London Mathematical Society Lecture Note Series

  • Date Published: March 2021
  • availability: In stock
  • format: Paperback
  • isbn: 9781108949538

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About the Authors
  • 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.

    • The first book on the theory of modules invariant under automorphisms of their envelopes and covers
    • Begins with the basics of ring and module theory, making it self-contained and suitable for graduate students
    • Contains plentiful examples and a whole chapter of open problems to which researchers can apply the theory
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    Reviews & endorsements

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

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    Product details

    • Date Published: March 2021
    • format: Paperback
    • isbn: 9781108949538
    • length: 232 pages
    • dimensions: 228 x 152 x 13 mm
    • weight: 0.35kg
    • availability: In stock
  • Table of Contents

    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

  • Authors

    Ashish K. Srivastava, St Louis University, Missouri
    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, National Research University 'Moscow Power Engineering Institute'
    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, Universidad de Murcia, Spain
    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.

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