This book presents a new homological approximation theory in the category of equivariant modules, unifying the Cohen-Macaulay approximations in commutative ring theory and Ringel's theory of Delta-good approximations for quasi-hereditary algebras and reductive groups. The book provides a detailed introduction to homological algebra, commutative ring theory and homological theory of comodules of coalgebras over an arbitrary base. It aims to overcome the difficulty of generalizing known homological results in representation theory.
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"The reviewer enthusiastically recommends it for anyone, including beginners, who wants to see the Auslander-Buchweitz approximations in action." Mathematical Reviews
Book Description
This book focuses on homological aspects of equivariant modules. It presents a new homological approximation theory in the category of equivariant modules, unifying the Cohen-Macaulay approximations in commutative ring theory and Ringel's theory of delta-good approximations for quasi-hereditary algebras and reductive groups. It also provides detailed introduction to homological algebra, commutative ring theory and homological theory of comodules of co-algebras over an arbitrary base. The book is primarily aimed at researchers but will also be suitable for graduate students.
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Inside This Book
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First Sentence:
(1.1.1) We denote the category of sets by Set, the category of groups by Grp, and the category of abelian groups by Ab or by zM. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
poset ideal, filtered inductive limit, finite flat dimension, highest weight theory, filtered inductive system, reductive group scheme, connected geometric fibers, determinantal rings, noetherian commutative ring, graded minimal free resolution, dualizing complex, cobar resolution, complete intersection ideal, locally noetherian schemes, equivariant modules, simple subquotient, noetherian objects, finite injective dimension, tilting modules, injective cogenerator, projective functor, noetherian local ring, full subcategory, exact category, abelian category Key Phrases - Capitalized Phrases (CAPs): (learn more)
R-finite R-projective, R-flat R-coalgebra, Background Materials, R-projective G-module, R-projective R-coalgebra, Cohen-Macaulay R-module, R-finite C-comodule, R-finite R-submodule, A-finite A-projective, U-module R-algebra, G-module A-module New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
(1.1.1) We denote the category of sets by Set, the category of groups by Grp, and the category of abelian groups by Ab or by zM. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
poset ideal, filtered inductive limit, finite flat dimension, highest weight theory, filtered inductive system, reductive group scheme, connected geometric fibers, determinantal rings, noetherian commutative ring, graded minimal free resolution, dualizing complex, cobar resolution, complete intersection ideal, locally noetherian schemes, equivariant modules, simple subquotient, noetherian objects, finite injective dimension, tilting modules, injective cogenerator, projective functor, noetherian local ring, full subcategory, exact category, abelian category Key Phrases - Capitalized Phrases (CAPs): (learn more)
R-finite R-projective, R-flat R-coalgebra, Background Materials, R-projective G-module, R-projective R-coalgebra, Cohen-Macaulay R-module, R-finite C-comodule, R-finite R-submodule, A-finite A-projective, U-module R-algebra, G-module A-module New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 18
books:
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- Hopf Algebras (Cambridge Tracts in Mathematics) by Eiichi Abe in Back Matter (1), and Back Matter (2)
- Representation Theory of Artin Algebras (Cambridge Studies in Advanced Mathematics) by Maurice Auslander in Back Matter
- Linear Algebraic Groups (Progress in Mathematics) by T.A. Springer in Back Matter
- An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics) by Charles A. Weibel in Back Matter
- Symmetric Functions and Hall Polynomials (Oxford Mathematical Monographs) by I. G. Macdonald in Back Matter
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