Description

Book Synopsis
This book provides an organized exposition of the current state of the theory of commutative semigroup cohomology, a theory which was originated by the author and has matured in the past few years.

The work contains a fundamental scientific study of questions in the theory. The various approaches to commutative semigroup cohomology are compared. The problems arising from definitions in higher dimensions are addressed. Computational methods are reviewed. The main application is the computation of extensions of commutative semigroups and their classification.

Previously the components of the theory were scattered among a number of research articles. This work combines all parts conveniently in one volume. It will be a valuable resource for future students of and researchers in commutative semigroup cohomology and related areas.




Table of Contents
- 1. The Beginning. - 2. Beck Cohomology. - 3. Symmetric Cohomology. - 4. Calvo-Cegarra Cohomology. - 5. The Third Cohomology Group. - 6. The Overpath Method. - 7. Symmetric Chains. - 8. Inheritance. - 9. Appendixes.

The Cohomology of Commutative Semigroups: An

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    A Paperback / softback by Pierre Antoine Grillet

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      Book details

      Publisher Springer International Publishing AG
      Published 29 September 2022
      ISBN-13 9783031082115
      978-3031082115
      ISBN-10 3031082117
      Also in:
      Mathematics Algebra Groups and group theory

      Description

      Book Synopsis
      This book provides an organized exposition of the current state of the theory of commutative semigroup cohomology, a theory which was originated by the author and has matured in the past few years.

      The work contains a fundamental scientific study of questions in the theory. The various approaches to commutative semigroup cohomology are compared. The problems arising from definitions in higher dimensions are addressed. Computational methods are reviewed. The main application is the computation of extensions of commutative semigroups and their classification.

      Previously the components of the theory were scattered among a number of research articles. This work combines all parts conveniently in one volume. It will be a valuable resource for future students of and researchers in commutative semigroup cohomology and related areas.




      Table of Contents
      - 1. The Beginning. - 2. Beck Cohomology. - 3. Symmetric Cohomology. - 4. Calvo-Cegarra Cohomology. - 5. The Third Cohomology Group. - 6. The Overpath Method. - 7. Symmetric Chains. - 8. Inheritance. - 9. Appendixes.

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