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34 relations: Abelian category, Adjoint functors, Advances in Mathematics, Algebra over a field, Algebraically closed field, Associative algebra, Cambridge University Press, Cluster algebra, Derived category, Endomorphism ring, Equivalence of categories, Ext functor, Field (mathematics), Finitely generated module, Functor, Global dimension, Grothendieck group, Hereditary ring, Injective cogenerator, Kernel (algebra), Mathematics, Memoirs of the American Mathematical Society, Module (mathematics), Morita equivalence, Projective module, Quiver (mathematics), Quotient module, Representation theory, Semidirect product, Springer Science+Business Media, Surjective function, Tor functor, Transactions of the American Mathematical Society, Triangulated category.
Abelian category
In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties.
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Adjoint functors
In mathematics, specifically category theory, adjunction is a possible relationship between two functors.
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Advances in Mathematics
Advances in Mathematics is a mathematics journal publishing research on pure mathematics.
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Algebra over a field
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.
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Algebraically closed field
In abstract algebra, an algebraically closed field F contains a root for every non-constant polynomial in F, the ring of polynomials in the variable x with coefficients in F.
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Associative algebra
In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Cluster algebra
Cluster algebras are a class of commutative rings introduced by.
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Derived category
In mathematics, the derived category D(A) of an abelian category A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on A. The construction proceeds on the basis that the objects of D(A) should be chain complexes in A, with two such chain complexes considered isomorphic when there is a chain map that induces an isomorphism on the level of homology of the chain complexes.
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Endomorphism ring
In abstract algebra, the endomorphism ring of an abelian group X, denoted by End(X), is the set of all endomorphisms of X (i.e., the set of all homomorphisms of X into itself) endowed with an addition operation defined by pointwise addition of functions and a multiplication operation defined by function composition.
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Equivalence of categories
In category theory, an abstract branch of mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are "essentially the same".
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Ext functor
In mathematics, the Ext functors of homological algebra are derived functors of Hom functors.
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Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
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Finitely generated module
In mathematics, a finitely generated module is a module that has a finite generating set.
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Functor
In mathematics, a functor is a map between categories.
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Global dimension
In ring theory and homological algebra, the global dimension (or global homological dimension; sometimes just called homological dimension) of a ring A denoted gl dim A, is a non-negative integer or infinity which is a homological invariant of the ring.
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Grothendieck group
In mathematics, the Grothendieck group construction in abstract algebra constructs an abelian group from a commutative monoid M in the most universal way in the sense that any abelian group containing a homomorphic image of M will also contain a homomorphic image of the Grothendieck group of M. The Grothendieck group construction takes its name from the more general construction in category theory, introduced by Alexander Grothendieck in his fundamental work of the mid-1950s that resulted in the development of K-theory, which led to his proof of the Grothendieck–Riemann–Roch theorem.
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Hereditary ring
In mathematics, especially in the area of abstract algebra known as module theory, a ring R is called hereditary if all submodules of projective modules over R are again projective.
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Injective cogenerator
In category theory, the concept of an injective cogenerator is drawn from examples such as Pontryagin duality.
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Kernel (algebra)
In the various branches of mathematics that fall under the heading of abstract algebra, the kernel of a homomorphism measures the degree to which the homomorphism fails to be injective.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Memoirs of the American Mathematical Society
Memoirs of the American Mathematical Society is a mathematical journal published in six volumes per year, totalling approximately 33 individually bound numbers, by the American Mathematical Society.
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Module (mathematics)
In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.
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Morita equivalence
In abstract algebra, Morita equivalence is a relationship defined between rings that preserves many ring-theoretic properties.
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Projective module
In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules.
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Quiver (mathematics)
In mathematics, a quiver is a directed graph where loops and multiple arrows between two vertices are allowed, i.e. a multidigraph.
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Quotient module
In algebra, given a module and a submodule, one can construct their quotient module.
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Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.
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Semidirect product
In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Surjective function
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
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Tor functor
In homological algebra, the Tor functors are the derived functors of the tensor product of modules over a ring.
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Transactions of the American Mathematical Society
The Transactions of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.
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Triangulated category
In mathematics, a triangulated category is a category together with the additional structure of a "translation functor" and a class of "distinguished triangles".
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Coxeter functor, Tilted algebra, Tilted functor, Tilted module, Tilting algebra, Tilting functor, Tilting module, Tilting object.
References
[1] https://en.wikipedia.org/wiki/Tilting_theory
