Invariance of Modules under Automorphisms of their Envelopes and Covers

Provides a unified treatment of the study of modules invariant under automorphisms of their envelopes and covers.

Ashish K. Srivastava (Author), Askar Tuganbaev (Author), Pedro A. Guil Asensio (Author)

9781108949538, Cambridge University Press

Paperback / softback, published 18 March 2021

232 pages
22.8 x 15.2 x 1.3 cm, 0.35 kg

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

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.

Subject Areas: Algebra [PBF], Mathematics [PB]