freely generated algebra

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• algebra — /al jeuh breuh/, n. 1. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. 2. any of… …   Universalium

• Jordan algebra — In mathematics, a Jordan algebra is defined in abstract algebra as a (usually nonassociative) algebra over a field with multiplication satisfying the following axioms:# xy = yx (commutative law) # (xy)(xx) = x(y(xx)) (Jordan identity)The product… …   Wikipedia

• Term algebra — In universal algebra, a term algebra is an algebraic structure which is freely generated from a signature specifying the operations of the algebra (including constants, which are nullary operations). For example, free magmas are isomorphic to… …   Wikipedia

• Computer algebra system — A computer algebra system (CAS) is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form. Contents 1 Symbolic manipulations 2 Additional capabilities …   Wikipedia

• Congruence lattice problem — In mathematics, the congruence lattice problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of some other lattice. The problem was posed by Robert P. Dilworth, and for many years it was one of the most …   Wikipedia

• Free group — In mathematics, a group G is called free if there is a subset S of G such that any element of G can be written in one and only one way as a product of finitely many elements of S and their inverses (disregarding trivial variations such as st 1 =… …   Wikipedia

• Generating set of a group — In abstract algebra, a generating set of a group is a subset that is not contained in any proper subgroup of the group. Equivalently, a generating set of a group is a subset such that every element of the group can be expressed as the combination …   Wikipedia

• Complete lattice — In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). Complete lattices appear in many applications in mathematics and computer science. Being a special instance of… …   Wikipedia

• Edge space — In the mathematical discipline of graph theory, the edge space and vertex space of an undirected graph are vector spaces defined in terms of the edge and vertex sets, respectively. These vector spaces make it possible to use techniques of linear… …   Wikipedia

• Hall polynomial — The Hall polynomials in mathematics were developed by Philip Hall in the 1950s in the study of group representations. These polynomials are the structure constants of a certain associative algebra, called the Hall algebra, which plays an… …   Wikipedia

• Small cancellation theory — In the mathematical subject of group theory, small cancellation theory studies groups given by group presentations satisfying small cancellation conditions, that is where defining relations have small overlaps with each other. It turns out that… …   Wikipedia