p-adic algebra
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Quaternion algebra — In mathematics, a quaternion algebra over a field, F , is a particular kind of central simple algebra, A , over F , namely such an algebra that has dimension 4, and therefore becomes the 2 times;2 matrix algebra over some field extension of F ,… … Wikipedia
Valuation (algebra) — In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field. They generalize to commutative algebra the notion of size… … Wikipedia
Hecke algebra — is the common name of several related types of associative rings in algebra and representation theory. The most familiar of these is the Hecke algebra of a Coxeter group , also known as Iwahori Hecke algebra, which is a one parameter deformation… … Wikipedia
Banach algebra — In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space. The algebra multiplication and the Banach… … Wikipedia
List of commutative algebra topics — Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative… … Wikipedia
Absolute value (algebra) — In mathematics, an absolute value is a function which measures the size of elements in a field or integral domain. More precisely, if D is an integral domain, then an absolute value is any mapping | thinsp; sdot; thinsp;| from D to the real… … Wikipedia
Commutative algebra — This page deals with the area of study. For algebras which are commutative, see algebra (disambiguation). Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both… … Wikipedia
p-adic order — In number theory, for a given prime number p, the p adic order or additive p adic valuation of a number n is the highest exponent ν such that pν divides n. It is commonly abbreviated νp(n). The most important application of the p adic order is in … Wikipedia
Affine Hecke algebra — DefinitionLet V be a Euclidean space of a finite dimension and Sigma an affine root system on V. An affine Hecke algebra is a certain associative algebra that deforms the group algebra mathbb{C} [W] of the Weyl group W of Sigma (the affine Weyl… … Wikipedia
Characteristic (algebra) — In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring s multiplicative identity element (1) in a sum to get the additive identity element (0); the ring is said… … Wikipedia
Lie group — Lie groups … Wikipedia
