# Trivial Extensions of Abelian Categories: Homological Algebra of Trivial Extensions of Abelian Catergories with Applications to Ring Theory (Lecture Notes in Mathematics) ebook

## by R.M. Fossum,P.A. Griffith,I. Reiten

Lecture Notes in Mathematics. Homological dimensions in A ⋉ F. Pages 52-86. Dominant dimension of finite algebras.

Lecture Notes in Mathematics. Trivial Extensions of Abelian Categories. Homological Algebra of Trivial Extensions of Abelian Catergories with Applications to Ring Theory. Representation dimension of finite algebras. Fossum, Dr. Robert M. (et a.

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This chapter discusses the trivial extensions of Abelian categories and applications to rings

Homological properties of nontrivial extensions of abelian categories by a functor are defined by the author, and the coherence of such categories are studied in. In the special case, the results obtained in this direction give new results for the category of modules over nontrivial extensions of rings by bimodules. Categorical, homological, and homotopical properties of algebraic objects. This chapter discusses the trivial extensions of Abelian categories and applications to rings. It discusses the homological dimension of a map f: FA → B in terms of the homological dimensions of A, B, and the derived functors LiFA.

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Abelian Groups, Rings, Modules, and Homological Algebra PURE AND APPLIED MATHEMATICS A. .

Abelian Groups, Rings, Modules, and Homological Algebra PURE AND APPLIED MATHEMATICS A Program of Monographs, Textboo. Analytic theory of Abelian varieties. Compactifying moduli spaces for abelian varieties (Lecture Notes in Mathematics). Vol, Moduli of Abelian Varieties.

Categories and homological algebra. An introduction to derived categories. If N is a submodule of M, it denes an equivalence relation mRm if and only if m − m ∈ N. One easily checks that the quotient set M/R is naturally endowed with a structure of a left A-module

Categories and homological algebra. One easily checks that the quotient set M/R is naturally endowed with a structure of a left A-module. This module is called the quotient module and is denoted M/N.

This is a timeline of category theory and related mathematics. Its scope ('related mathematics') is taken as: Categories of abstract algebraic structures including representation theory and universal algebra; Homological algebra; Homotopical algebra; Topology using categories, including algebraic topology, categorical topology, quantum topology, low-dimensional topology; Categorical logic and set theory in the categorical context such as algebraic set theory;