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This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it  will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.

Algebra. --- Algebraic geometry. --- Commutative algebra. --- Mathematics. --- Commutative algebra --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Math --- Associative rings. --- Rings (Algebra). --- Commutative rings. --- Commutative Rings and Algebras. --- Algebraic Geometry. --- Associative Rings and Algebras. --- Science --- Mathematical analysis --- Geometry, algebraic. --- Algebraic geometry --- Geometry --- Rings (Algebra) --- Algebraic rings --- Ring theory --- Algebraic fields

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This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it  will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.

Mathematics --- Ordered algebraic structures --- Algebra --- Algebraic geometry --- Geometry --- algebra --- landmeetkunde --- wiskunde --- geometrie

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This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957. The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics.

Algebra --- Mathematics --- Physical Sciences & Mathematics --- Mathematics. --- Algebraic geometry. --- Category theory (Mathematics). --- Homological algebra. --- Commutative algebra. --- Commutative rings. --- Physics. --- Commutative Rings and Algebras. --- Algebraic Geometry. --- Category Theory, Homological Algebra. --- Theoretical, Mathematical and Computational Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Rings (Algebra) --- Homological algebra --- Algebra, Abstract --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Algebraic geometry --- Geometry --- Math --- Science --- Algebra. --- Geometry, algebraic. --- Mathematical analysis --- Syzygies (Mathematics) --- Resolvents (Mathematics) --- Geometry, Algebraic. --- Syzygy theory (Mathematics) --- Categories (Mathematics) --- Resolvent of an operator --- Matrices --- Operator theory --- Mathematical physics. --- Physical mathematics --- Physics --- Algebra, Homological.

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This contributed volume is a follow-up to the 2013 volume of the same title, published in honor of noted Algebraist David Eisenbud's 65th birthday. It brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Category Theory, Combinatorics, Computational Algebra, Homological Algebra, Hyperplane Arrangements, and Non-commutative Algebra. The book aims to showcase the area and aid junior mathematicians and researchers who are new to the field in broadening their background and gaining a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.

Ordered algebraic structures --- Algebra --- Geometry --- algebra --- landmeetkunde --- Àlgebra commutativa --- Anells commutatius --- Commutative algebra.