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A group or other algebraic object is said to be Abelian (sometimes written in lower case, i.e., "abelian") if the law of commutativity always holds. The term is named after ...

Let M(X) denote the group of all invertible maps X->X and let G be any group. A homomorphism theta:G->M(X) is called an action of G on X. Therefore, theta satisfies 1. For ...

An additive category is a category for which the morphism sets have the structure of Abelian groups. It satisfies some, but not all the properties of an Abelian category.

The restricted topological group direct product of the group G_(k_nu) with distinct invariant open subgroups G_(0_nu).

The set of all nonsingular affine transformations of a translation in space constitutes a group known as the affine group. The affine group contains the full linear group and ...

"Aggregate" is an archaic word for infinite sets such as those considered by Georg Cantor. The term is sometimes also used to refer to a finite or infinite set in which ...

The order ideal in Lambda, the ring of integral laurent polynomials, associated with an Alexander matrix for a knot K. Any generator of a principal Alexander ideal is called ...

An Alexander matrix is a presentation matrix for the Alexander invariant H_1(X^~) of a knot K. If V is a Seifert matrix for a tame knot K in S^3, then V^(T)-tV and V-tV^(T) ...

The field F^_ is called an algebraic closure of F if F^_ is algebraic over F and if every polynomial f(x) in F[x] splits completely over F^_, so that F^_ can be said to ...

An extension F of a field K is said to be algebraic if every element of F is algebraic over K (i.e., is the root of a nonzero polynomial with coefficients in K).