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Invariance of Modules under Automorphisms of their Envelopes and Covers: 466 (London Mathematical Society Lecture Note Series, Series Number 466)

Invariance of Modules under Automorphisms of their Envelopes and Covers: 466 (London Mathematical Society Lecture Note Series, Series Number 466)

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Ashish K. Srivastava
Cambridge University Press, 3/18/2021
EAN 9781108949538, ISBN10: 1108949533

Paperback, 234 pages, 22.9 x 15.2 x 1.3 cm
Language: English
Originally published in English

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.

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.