Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Ring_theory> ?p ?o }
- Ring_theory abstract "In abstract algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings (group rings, division rings, universal enveloping algebras), as well as an array of properties that proved to be of interest both within the theory itself and for its applications, such as homological properties and polynomial identities.Commutative rings are much better understood than noncommutative ones. Algebraic geometry and algebraic number theory, which provide many natural examples of commutative rings, have driven much of the development of commutative ring theory, which is now, under the name of commutative algebra, a major area of modern mathematics. Because these three fields (algebraic geometry, algebraic number theory and commutative algebra) are so intimately connected it is usually difficult and meaningless to decide which field a particular result belongs to. For example, Hilbert's Nullstellensatz is a theorem which is fundamental for algebraic geometry, and is stated and proved in terms of commutative algebra. Similarly, Fermat's last theorem is stated in terms of elementary arithmetic, which is a part of commutative algebra, but its proof involves deep results of both algebraic number theory and algebraic geometry.Noncommutative rings are quite different in flavour, since more unusual behavior can arise. While the theory has developed in its own right, a fairly recent trend has sought to parallel the commutative development by building the theory of certain classes of noncommutative rings in a geometric fashion as if they were rings of functions on (non-existent) 'noncommutative spaces'. This trend started in the 1980s with the development of noncommutative geometry and with the discovery of quantum groups. It has led to a better understanding of noncommutative rings, especially noncommutative Noetherian rings. (Goodearl 1989)For the definitions of a ring and basic concepts and their properties, see ring (mathematics). The definitions of terms used throughout ring theory may be found in the glossary of ring theory.".
- Ring_theory wikiPageExternalLink abstract.ups.edu.
- Ring_theory wikiPageExternalLink Kbook.html.
- Ring_theory wikiPageExternalLink Ring_theory.html.
- Ring_theory wikiPageExternalLink book.
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- Ring_theory wikiPageRevisionID "680656369".
- Ring_theory wikiPageWikiLink Abstract_algebra.
- Ring_theory wikiPageWikiLink Affine_algebraic_variety.
- Ring_theory wikiPageWikiLink Affine_variety.
- Ring_theory wikiPageWikiLink Alexander_Grothendieck.
- Ring_theory wikiPageWikiLink Algebra.
- Ring_theory wikiPageWikiLink Algebra_over_a_field.
- Ring_theory wikiPageWikiLink Algebra_representation.
- Ring_theory wikiPageWikiLink Algebraic_geometry.
- Ring_theory wikiPageWikiLink Algebraic_number_theory.
- Ring_theory wikiPageWikiLink Algebraic_operation.
- Ring_theory wikiPageWikiLink Algebraic_structure.
- Ring_theory wikiPageWikiLink Annihilator_(ring_theory).
- Ring_theory wikiPageWikiLink Arithmetic.
- Ring_theory wikiPageWikiLink Artinian_ring.
- Ring_theory wikiPageWikiLink Artin–Wedderburn_theorem.
- Ring_theory wikiPageWikiLink Ascending_chain_condition.
- Ring_theory wikiPageWikiLink Associative_algebra.
- Ring_theory wikiPageWikiLink Bicomplex_number.
- Ring_theory wikiPageWikiLink Biquaternion.
- Ring_theory wikiPageWikiLink Category:Ring_theory.
- Ring_theory wikiPageWikiLink Category_theory.
- Ring_theory wikiPageWikiLink Catenary_ring.
- Ring_theory wikiPageWikiLink Cohen–Macaulay_ring.
- Ring_theory wikiPageWikiLink Commutative.
- Ring_theory wikiPageWikiLink Commutative_algebra.
- Ring_theory wikiPageWikiLink Commutative_property.
- Ring_theory wikiPageWikiLink Commutative_ring.
- Ring_theory wikiPageWikiLink Coordinate_ring.
- Ring_theory wikiPageWikiLink Coquaternion.
- Ring_theory wikiPageWikiLink Depth_(ring_theory).
- Ring_theory wikiPageWikiLink Direct_sum_of_modules.
- Ring_theory wikiPageWikiLink Division_ring.
- Ring_theory wikiPageWikiLink Divisor_class_group.
- Ring_theory wikiPageWikiLink Domain_(ring_theory).
- Ring_theory wikiPageWikiLink Element_(mathematics).
- Ring_theory wikiPageWikiLink Element_(set_theory).
- Ring_theory wikiPageWikiLink Elementary_symmetric_polynomial.
- Ring_theory wikiPageWikiLink Emil_Artin.
- Ring_theory wikiPageWikiLink Emmy_Noether.
- Ring_theory wikiPageWikiLink Endomorphism.
- Ring_theory wikiPageWikiLink Endomorphism_ring.
- Ring_theory wikiPageWikiLink Euclidean_domain.
- Ring_theory wikiPageWikiLink Fermats_Last_Theorem.
- Ring_theory wikiPageWikiLink Fermats_last_theorem.
- Ring_theory wikiPageWikiLink Field_(mathematics).
- Ring_theory wikiPageWikiLink Finiteness_of_class_number.
- Ring_theory wikiPageWikiLink Fractional_ideal.
- Ring_theory wikiPageWikiLink Function_(mathematics).
- Ring_theory wikiPageWikiLink Fundamental_theorem_of_symmetric_polynomials.
- Ring_theory wikiPageWikiLink GNU_Free_Documentation_License.
- Ring_theory wikiPageWikiLink Geometry.
- Ring_theory wikiPageWikiLink Global_dimension.
- Ring_theory wikiPageWikiLink Glossary_of_ring_theory.
- Ring_theory wikiPageWikiLink Goldie_ring.
- Ring_theory wikiPageWikiLink Goldies_theorem.
- Ring_theory wikiPageWikiLink Graduate_Studies_in_Mathematics.
- Ring_theory wikiPageWikiLink Greatest_common_divisor.
- Ring_theory wikiPageWikiLink Grothendieck_group.
- Ring_theory wikiPageWikiLink Group_(mathematics).
- Ring_theory wikiPageWikiLink Group_completion.
- Ring_theory wikiPageWikiLink Group_representation.
- Ring_theory wikiPageWikiLink Group_ring.
- Ring_theory wikiPageWikiLink Height_(ring_theory).
- Ring_theory wikiPageWikiLink Hilbert_polynomial.
- Ring_theory wikiPageWikiLink Hilbert_series_and_Hilbert_polynomial.
- Ring_theory wikiPageWikiLink Hilberts_Nullstellensatz.
- Ring_theory wikiPageWikiLink Homogeneous_coordinate_ring.
- Ring_theory wikiPageWikiLink Homological_algebra.
- Ring_theory wikiPageWikiLink Hopkins–Levitzki_theorem.
- Ring_theory wikiPageWikiLink Hypercomplex_number.
- Ring_theory wikiPageWikiLink Ian_G._Macdonald.
- Ring_theory wikiPageWikiLink Ideal_(ring_theory).
- Ring_theory wikiPageWikiLink Ideal_class_group.
- Ring_theory wikiPageWikiLink Ideal_theory.
- Ring_theory wikiPageWikiLink Integer.
- Ring_theory wikiPageWikiLink Integral_domain.
- Ring_theory wikiPageWikiLink Integral_element.
- Ring_theory wikiPageWikiLink Integral_extension.
- Ring_theory wikiPageWikiLink Invariant_theory.
- Ring_theory wikiPageWikiLink Irving_Kaplansky.
- Ring_theory wikiPageWikiLink Isomorphism_theorem.
- Ring_theory wikiPageWikiLink Jacobson_density_theorem.
- Ring_theory wikiPageWikiLink Jacobson_radical.
- Ring_theory wikiPageWikiLink James_Cockle.
- Ring_theory wikiPageWikiLink James_Cockle_(lawyer).
- Ring_theory wikiPageWikiLink Joseph_Wedderburn.
- Ring_theory wikiPageWikiLink Klein_four-group.
- Ring_theory wikiPageWikiLink Krull_dimension.
- Ring_theory wikiPageWikiLink Lie_algebra.
- Ring_theory wikiPageWikiLink Linear_map.
- Ring_theory wikiPageWikiLink Linear_transformation.