Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Ideal_(ring_theory)> ?p ?o }
- Ideal_(ring_theory) abstract "In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any other integer results in another even number; these closure and absorption properties are the defining properties of an ideal. An ideal can be used to construct a quotient ring similarly to the way that, in group theory, a normal subgroup can be used to construct a quotient group.Among the integers, the ideals correspond one-for-one with the non-negative integers: in this ring, every ideal is a principal ideal consisting of the multiples of a single non-negative number. However, in other rings, the ideals may be distinct from the ring elements, and certain properties of integers, when generalized to rings, attach more naturally to the ideals than to the elements of the ring. For instance, the prime ideals of a ring are analogous to prime numbers, and the Chinese remainder theorem can be generalized to ideals. There is a version of unique prime factorization for the ideals of a Dedekind domain (a type of ring important in number theory).The concept of an order ideal in order theory is derived from the notion of ideal in ring theory. A fractional ideal is a generalization of an ideal, and the usual ideals are sometimes called integral ideals for clarity.".
- Ideal_(ring_theory) wikiPageID "25977".
- Ideal_(ring_theory) wikiPageLength "21011".
- Ideal_(ring_theory) wikiPageOutDegree "118".
- Ideal_(ring_theory) wikiPageRevisionID "682197511".
- Ideal_(ring_theory) wikiPageWikiLink Abstract_algebra.
- Ideal_(ring_theory) wikiPageWikiLink Additive_group.
- Ideal_(ring_theory) wikiPageWikiLink Annihilator_(ring_theory).
- Ideal_(ring_theory) wikiPageWikiLink Artinian_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Bimodule.
- Ideal_(ring_theory) wikiPageWikiLink Boolean_prime_ideal_theorem.
- Ideal_(ring_theory) wikiPageWikiLink Bounded_operator.
- Ideal_(ring_theory) wikiPageWikiLink Bounded_operators.
- Ideal_(ring_theory) wikiPageWikiLink Category:Algebraic_structures.
- Ideal_(ring_theory) wikiPageWikiLink Category:Ideals.
- Ideal_(ring_theory) wikiPageWikiLink Chinese_remainder_theorem.
- Ideal_(ring_theory) wikiPageWikiLink Closure_(mathematics).
- Ideal_(ring_theory) wikiPageWikiLink Compact_operator.
- Ideal_(ring_theory) wikiPageWikiLink Complete_lattice.
- Ideal_(ring_theory) wikiPageWikiLink Congruence_relation.
- Ideal_(ring_theory) wikiPageWikiLink Continuous_function.
- Ideal_(ring_theory) wikiPageWikiLink Coset.
- Ideal_(ring_theory) wikiPageWikiLink David_Hilbert.
- Ideal_(ring_theory) wikiPageWikiLink Dedekind_domain.
- Ideal_(ring_theory) wikiPageWikiLink Distributive_lattice.
- Ideal_(ring_theory) wikiPageWikiLink Division_ring.
- Ideal_(ring_theory) wikiPageWikiLink Emmy_Noether.
- Ideal_(ring_theory) wikiPageWikiLink Empty_set.
- Ideal_(ring_theory) wikiPageWikiLink Empty_sum.
- Ideal_(ring_theory) wikiPageWikiLink Ernst_Kummer.
- Ideal_(ring_theory) wikiPageWikiLink Even_numbers.
- Ideal_(ring_theory) wikiPageWikiLink Factor_ring.
- Ideal_(ring_theory) wikiPageWikiLink Field_(mathematics).
- Ideal_(ring_theory) wikiPageWikiLink Field_of_fractions.
- Ideal_(ring_theory) wikiPageWikiLink Finitely_generated_module.
- Ideal_(ring_theory) wikiPageWikiLink Fractional_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Fundamental_theorem_of_arithmetic.
- Ideal_(ring_theory) wikiPageWikiLink Group_theory.
- Ideal_(ring_theory) wikiPageWikiLink Homomorphism.
- Ideal_(ring_theory) wikiPageWikiLink Homomorphisms.
- Ideal_(ring_theory) wikiPageWikiLink Ideal_(order_theory).
- Ideal_(ring_theory) wikiPageWikiLink Ideal_norm.
- Ideal_(ring_theory) wikiPageWikiLink Ideal_number.
- Ideal_(ring_theory) wikiPageWikiLink Ideal_quotient.
- Ideal_(ring_theory) wikiPageWikiLink Ideal_theory.
- Ideal_(ring_theory) wikiPageWikiLink Idealizer.
- Ideal_(ring_theory) wikiPageWikiLink Integer.
- Ideal_(ring_theory) wikiPageWikiLink Integral_domain.
- Ideal_(ring_theory) wikiPageWikiLink Intersection_(set_theory).
- Ideal_(ring_theory) wikiPageWikiLink Invariant_(mathematics).
- Ideal_(ring_theory) wikiPageWikiLink Invertible_element.
- Ideal_(ring_theory) wikiPageWikiLink Invertible_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Irreducible_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Isomorphism_theorem.
- Ideal_(ring_theory) wikiPageWikiLink Join_(lattice_theory).
- Ideal_(ring_theory) wikiPageWikiLink Kernel_(algebra).
- Ideal_(ring_theory) wikiPageWikiLink Krulls_theorem.
- Ideal_(ring_theory) wikiPageWikiLink Lattice_(order).
- Ideal_(ring_theory) wikiPageWikiLink Matrix_(mathematics).
- Ideal_(ring_theory) wikiPageWikiLink Maximal_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Meet_(lattice_theory).
- Ideal_(ring_theory) wikiPageWikiLink Michiel_Hazewinkel.
- Ideal_(ring_theory) wikiPageWikiLink Minimal_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Modular_arithmetic.
- Ideal_(ring_theory) wikiPageWikiLink Modular_lattice.
- Ideal_(ring_theory) wikiPageWikiLink Module_(mathematics).
- Ideal_(ring_theory) wikiPageWikiLink Natural_number.
- Ideal_(ring_theory) wikiPageWikiLink Nil_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Noether_isomorphism_theorem.
- Ideal_(ring_theory) wikiPageWikiLink Non-negative_integer.
- Ideal_(ring_theory) wikiPageWikiLink Noncommutative_ring.
- Ideal_(ring_theory) wikiPageWikiLink Normal_subgroup.
- Ideal_(ring_theory) wikiPageWikiLink Number_theory.
- Ideal_(ring_theory) wikiPageWikiLink Opposite_ring.
- Ideal_(ring_theory) wikiPageWikiLink Order_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Order_theory.
- Ideal_(ring_theory) wikiPageWikiLink Parity_(mathematics).
- Ideal_(ring_theory) wikiPageWikiLink Partially_ordered_set.
- Ideal_(ring_theory) wikiPageWikiLink Pointwise_multiplication.
- Ideal_(ring_theory) wikiPageWikiLink Pointwise_product.
- Ideal_(ring_theory) wikiPageWikiLink Polynomial.
- Ideal_(ring_theory) wikiPageWikiLink Primary_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Prime_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Prime_number.
- Ideal_(ring_theory) wikiPageWikiLink Prime_ring.
- Ideal_(ring_theory) wikiPageWikiLink Primitive_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Primitive_ring.
- Ideal_(ring_theory) wikiPageWikiLink Principal_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Principal_ideal_domain.
- Ideal_(ring_theory) wikiPageWikiLink Pseudo-ring.
- Ideal_(ring_theory) wikiPageWikiLink Quotient_field.
- Ideal_(ring_theory) wikiPageWikiLink Quotient_group.
- Ideal_(ring_theory) wikiPageWikiLink Quotient_ring.
- Ideal_(ring_theory) wikiPageWikiLink Radical_of_an_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Reduced_ring.
- Ideal_(ring_theory) wikiPageWikiLink Regular_ideal.
- Ideal_(ring_theory) wikiPageWikiLink Richard_Dedekind.
- Ideal_(ring_theory) wikiPageWikiLink Ring_(mathematics).
- Ideal_(ring_theory) wikiPageWikiLink Ring_homomorphism.
- Ideal_(ring_theory) wikiPageWikiLink Ring_theory.