Ring (mathematics)
Ring (mathematics) In mathematics, a ring is an algebraic structure in which addition ... defined and have properties listed below. A ring is a generalization of the integers, which are one example of a ring. Other examples include the polynomials and ...
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Commutative ring
Commutative ring In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation obeys the ... and b are any elements of the ring, then a�b=b�a. The study of ...
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Ring theory
Ring theory In mathematics, ring theory is the study of rings, algebraic ... similar properties to those familiar from the integers. Please refer to the glossary of ring theory for the definitions of terms used throughout ring theory. History The study of rings ...
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Topological ring
Topological ring In mathematics, a topological ring is a ring R which is also a topological space ... is common: one starts with a commutative ring R containing an ideal I, and then ... U. This turns R into a topological ring. The I-adic topology is Hausdorff ...
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Noetherian ring
Noetherian ring In abstract algebra, a Noetherian ring is a ring that satisfies the ascending chain condition on ... distinguish between three very similar concepts: A ring is left-Noetherian if it satisfies the ... ascending chain condition on left ideals. A ring is right-Noetherian if it satisfies ...
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Kummer ring
Kummer ring In abstract algebra, a Kummer ring $\backslash mathbb\{Z\}(\backslash zeta)$ is a subring of the ring of complex numbers, such that each of ... n 0 through n m-1 are integers. Such Kummer ring is an extension of $\backslash mathbb\{\; ...$
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Polynomial ring
Polynomial ring In abstract algebra, a polynomial ring is the set of polynomials in one ... or more variables with coefficients in a ring. Definition of a polynomial In real analysis ... definition cannot be adapted to a general ring, however. For example, over the ring Z/2Z of integers modulo 2, ...
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Ring homomorphism
Ring homomorphism In abstract algebra, a ring homomorphism is a function between two rings ... R and S are rings, then a ring homomorphism is a function f : R → ... condition is dropped.) The composition of two ring homomorphisms is a ring homomorphism. It follows that the class ...
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Monoid ring
Monoid ring In abstract algebra, a monoid ring is a procedure which constructs a new ring from a given ring and a monoid. Let R be a ring and G be a monoid. We ...
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Ring (algebra)   (translated from Russian)
Ring (algebra) In abstraktnoy algebra , the concept of ring, the natural generalization the integers. Only it is more precise, this mnozhestvo ... which resemble the addition and the multiplication integers. Content Determinations Ring? - this mnozhestvo R, on which are ...
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