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A proving technique in homological algebra which consists in looking for equivalent map compositions in commutative diagrams, and in exploiting the properties of injective, ...

Let X be an infinite set of urelements, and let V(^*X) be an enlargement of V(X). Let H in V(^*X) be an algebra. Then H is hyperfinitely generated provided that it has a ...

Let A be a commutative complex Banach algebra. The space of all characters on A is called the maximal ideal space (or character space) of A. This space equipped with the ...

Let M be a sigma-algebra M, and let lambda_1 and lambda_2 be measures on M. If there exists a pair of disjoint sets A and B such that lambda_1 is concentrated on A and ...

Let pi be a unitary representation of a group G on a separable Hilbert space, and let R(pi) be the smallest weakly closed algebra of bounded linear operators containing all ...

There are at least two statements known as Schur's lemma. 1. The endomorphism ring of an irreducible module is a division algebra. 2. Let V, W be irreducible (linear) ...

In an exterior algebra ^ V, a top-dimensional form has degree n where n=dimV. Any form of higher degree must be zero. For example, if V=R^4 then alpha=e_1 ^ e_2 ^ e_3 ^ e_4 ...

Let A be a unital C^*-algebra. An element u in A is called unitary if u^*u=uu^*=1. For example, for each self-adjoint element a in A, the element ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

Given a group G, the algebra CG is a vector space CG={suma_ig_i|a_i in C,g_i in G} of finite sums of elements of G, with multiplication defined by g·h=gh, the group ...