algebra of infinite order

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• Order theory — For a topical guide to this subject, see Outline of order theory. Order theory is a branch of mathematics which investigates our intuitive notion of order using binary relations. It provides a formal framework for describing statements such as… …   Wikipedia

• Algebra — This article is about the branch of mathematics. For other uses, see Algebra (disambiguation). Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from… …   Wikipedia

• Infinite product — In mathematics, for a sequence of numbers a 1, a 2, a 3, ... the infinite product :prod {n=1}^{infty} a n = a 1 ; a 2 ; a 3 cdotsis defined to be the limit of the partial products a 1 a 2... a n as n increases without bound. The product is said… …   Wikipedia

• Order topology — In mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order …   Wikipedia

• Von Neumann algebra — In mathematics, a von Neumann algebra or W* algebra is a * algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. They were originally introduced by John von Neumann,… …   Wikipedia

• Complete Boolean algebra — This article is about a type of mathematical structure. For complete sets of Boolean operators, see Functional completeness. In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound) …   Wikipedia

• Lie algebra — In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term… …   Wikipedia

• 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

• Kac–Moody algebra — In mathematics, a Kac–Moody algebra is a Lie algebra, usually infinite dimensional, that can be defined by generators and relations through a generalized Cartan matrix. Kac–Moody algebras are named after Victor Kac and Robert Moody, who… …   Wikipedia

• Torsion (algebra) — In abstract algebra, the term torsion refers to a number of concepts related to elements of finite order in groups and to the failure of modules to be free. Definition Let G be a group. An element g of G is called a torsion element if g has… …   Wikipedia

• List of order theory topics — Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of ordering, providing a framework for saying when one thing is less than or precedes another. An alphabetical list of many… …   Wikipedia