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Ordered algebraic structures --- Artin rings. --- Artin algebras. --- Representations of algebras.

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Ordered algebraic structures --- Artin rings. --- Representations of rings (Algebra) --- Partially ordered sets --- Representations of algebras --- Anneaux artiniens. --- Ensembles partiellement ordonnés. --- Représentations d'algèbres. --- Artin rings --- Rings (Algebra) --- Algebra --- Posets --- Sets, Partially ordered --- Ordered sets --- Artinian rings --- Rings, Artin --- Rings, Artinian --- Associative rings --- Commutative rings

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Associative algebras --- Grothendieck groups --- Representations of algebras

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This book is an introduction to the contemporary representation theory of Artin algebras, by three very distinguished practitioners in the field. Beyond assuming some first-year graduate algebra and basic homological algebra, the presentation is entirely self-contained, so the book is a suitable introduction for any mathematician (especially graduate students) to this field. The main aim of the book is to illustrate how the theory of almost split sequences is used in the representation theory of Artin algebras. However, other foundational aspects of the subject are developed. These results give concrete illustrations of some of the more abstract concepts and theorems. The book includes complete proofs of all theorems, and numerous exercises.

Artin rings. --- Artin algebras. --- Representations of algebras.

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This book features survey and research papers from The Abel Symposium 2011, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in representation theory of quivers and algebras. Algebras, Quivers and Representations is targeted at researchers and graduate students in algebra, representation theory and triangulated categories.

Representations of algebras. --- Mathematics. --- Algebra. --- Algebraic geometry. --- Associative rings. --- Rings (Algebra). --- Category theory (Mathematics). --- Homological algebra. --- Commutative algebra. --- Commutative rings. --- Dynamics. --- Ergodic theory. --- Commutative Rings and Algebras. --- Algebraic Geometry. --- Associative Rings and Algebras. --- Category Theory, Homological Algebra. --- Dynamical Systems and Ergodic Theory. --- Algebra --- Geometry, algebraic. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Algebraic geometry --- Geometry --- Mathematics --- Mathematical analysis --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Homological algebra --- Algebra, Abstract --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra)