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An acnode, also called an isolated point or hermit point, of a curve is a point that satisfies the equation of the curve but has no neighboring points that also lie on the ...

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 ...

The identity element of an additive group G, usually denoted 0. In the additive group of vectors, the additive identity is the zero vector 0, in the additive group of ...

In an additive group G, the additive inverse of an element a is the element a^' such that a+a^'=a^'+a=0, where 0 is the additive identity of G. Usually, the additive inverse ...

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

A curve which has at least multiplicity r_i-1 at each point where a given curve (having only ordinary singular points and cusps) has a multiplicity r_i is called the adjoint ...

An Abelian variety which is canonically attached to an algebraic variety which is the solution to a certain universal problem. The Albanese variety is dual to the Picard ...

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 algebraic expression in variables {x_1,...,x_n} is an expression constructed with the variables and algebraic numbers using addition, multiplication, and rational powers.

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).