Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Ring_(mathematics)> ?p ?o }
- Ring_(mathematics) abstract "In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra. It consists of a set equipped with two binary operations that generalize the arithmetic operations of addition and multiplication. Through this generalization, theorems from arithmetic are extended to non-numerical objects such as polynomials, series, matrices and functions.The conceptualization of rings started in the 1870s and completed in the 1920s. Key contributors include Dedekind, Hilbert, Fraenkel, and Noether. Rings were first formalized as a generalization of Dedekind domains that occur in number theory, and of polynomial rings and rings of invariants that occur in algebraic geometry and invariant theory. Afterward, they also proved to be useful in other branches of mathematics such as geometry and mathematical analysis.A ring is an abelian group with a second binary operation that is associative, is distributive over the abelian group operation, and has an identity element. By extension from the integers, the abelian group operation is called addition and the second binary operation is called multiplication.Whether a ring is commutative or not (i.e., whether the order in which two elements are multiplied changes or not the result) has profound implications on its behavior as an abstract object. As a result, commutative ring theory, commonly known as commutative algebra, is a key topic in ring theory. Its development has been greatly influenced by problems and ideas occurring naturally in algebraic number theory and algebraic geometry. Examples of commutative rings include the set of integers equipped with the addition and multiplication operations, the set of polynomials equipped with the addition and multiplication of functions, the coordinate ring of an affine algebraic variety, and the ring of integers of a number field. Examples of noncommutative rings include the ring of n × n real square matrices with n ≥ 2, group rings in representation theory, operator algebras in functional analysis, rings of differential operators in the theory of differential operators, and the cohomology ring of a topological space in topology.".
- Ring_(mathematics) thumbnail Chapitel_IX._of_Die_Theorie_der_algebraischen_Zahlkörper.png?width=300.
- Ring_(mathematics) wikiPageExternalLink cft.html.
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- Ring_(mathematics) wikiPageExternalLink Kbook.html.
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- Ring_(mathematics) wikiPageWikiLink 1_(number).
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- Ring_(mathematics) wikiPageWikiLink Abraham_Fraenkel.
- Ring_(mathematics) wikiPageWikiLink Abstract_algebra.
- Ring_(mathematics) wikiPageWikiLink Addition.
- Ring_(mathematics) wikiPageWikiLink Additive_group.
- Ring_(mathematics) wikiPageWikiLink Additive_identity.
- Ring_(mathematics) wikiPageWikiLink Additive_inverse.
- Ring_(mathematics) wikiPageWikiLink Adele_ring.
- Ring_(mathematics) wikiPageWikiLink Affine_variety.
- Ring_(mathematics) wikiPageWikiLink Algebra_over_a_field.
- Ring_(mathematics) wikiPageWikiLink Algebra_representation.
- Ring_(mathematics) wikiPageWikiLink Algebraic_closure.
- Ring_(mathematics) wikiPageWikiLink Algebraic_combinatorics.
- Ring_(mathematics) wikiPageWikiLink Algebraic_geometry.
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- Ring_(mathematics) wikiPageWikiLink Algebraic_number_field.
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- Ring_(mathematics) wikiPageWikiLink Associative_property.
- Ring_(mathematics) wikiPageWikiLink Automorphism.
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- Ring_(mathematics) wikiPageWikiLink Banach_algebra.
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- Ring_(mathematics) wikiPageWikiLink Brauer_group.
- Ring_(mathematics) wikiPageWikiLink Burnside_ring.
- Ring_(mathematics) wikiPageWikiLink Cambridge_University_Press.
- Ring_(mathematics) wikiPageWikiLink Canonical_bundle.
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- Ring_(mathematics) wikiPageWikiLink Cartan–Brauer–Hua_theorem.
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- Ring_(mathematics) wikiPageWikiLink Categorical_ring.
- Ring_(mathematics) wikiPageWikiLink Category:Algebraic_structures.
- Ring_(mathematics) wikiPageWikiLink Category:Ring_theory.
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- Ring_(mathematics) wikiPageWikiLink Center_(algebra).
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- Ring_(mathematics) wikiPageWikiLink Change_of_rings.
- Ring_(mathematics) wikiPageWikiLink Change_of_variables.
- Ring_(mathematics) wikiPageWikiLink Character_theory.
- Ring_(mathematics) wikiPageWikiLink Characteristic_(algebra).
- Ring_(mathematics) wikiPageWikiLink Characteristic_class.
- Ring_(mathematics) wikiPageWikiLink Chinese_remainder_theorem.
- Ring_(mathematics) wikiPageWikiLink Clifford_algebra.
- Ring_(mathematics) wikiPageWikiLink Cohen_structure_theorem.
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- Ring_(mathematics) wikiPageWikiLink Cohomology_ring.
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- Ring_(mathematics) wikiPageWikiLink Commutative_ring.
- Ring_(mathematics) wikiPageWikiLink Completion_(algebra).
- Ring_(mathematics) wikiPageWikiLink Continuous_function.
- Ring_(mathematics) wikiPageWikiLink Convolution.
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- Ring_(mathematics) wikiPageWikiLink Cyclic_module.
- Ring_(mathematics) wikiPageWikiLink David_Hilbert.
- Ring_(mathematics) wikiPageWikiLink Decimal.
- Ring_(mathematics) wikiPageWikiLink Dedekind_domain.
- Ring_(mathematics) wikiPageWikiLink Differential_algebra.
- Ring_(mathematics) wikiPageWikiLink Differential_operator.
- Ring_(mathematics) wikiPageWikiLink Dirac_delta_function.
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- Ring_(mathematics) wikiPageWikiLink Discrete_valuation_ring.
- Ring_(mathematics) wikiPageWikiLink Distributive_property.
- Ring_(mathematics) wikiPageWikiLink Division_ring.
- Ring_(mathematics) wikiPageWikiLink Domain_(ring_theory).
- Ring_(mathematics) wikiPageWikiLink Domain_of_a_function.
- Ring_(mathematics) wikiPageWikiLink Eisenstein_integer.
- Ring_(mathematics) wikiPageWikiLink Emmy_Noether.
- Ring_(mathematics) wikiPageWikiLink Endomorphism.
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- Ring_(mathematics) wikiPageWikiLink Epimorphism.
- Ring_(mathematics) wikiPageWikiLink Ernst_Kummer.
- Ring_(mathematics) wikiPageWikiLink Euclidean_domain.
- Ring_(mathematics) wikiPageWikiLink Euclidean_topology.
- Ring_(mathematics) wikiPageWikiLink Excellent_ring.