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Let K be an algebraically closed field and let I be an ideal in K(x), where x=(x_1,x_2,...,x_n) is a finite set of indeterminates. Let p in K(x) be such that for any ...

In a chain complex of modules ...->C_(i+1)->^(d_(i+1))C_i->^(d_i)C_(i-1)->..., the module B_i of i-boundaries is the image of d_(i+1). It is a submodule of C_i and is ...

If F is a sigma-algebra and A is a subset of X, then A is called measurable if A is a member of F. X need not have, a priori, a topological structure. Even if it does, there ...

A quantity which is either 0 (zero) or negative, i.e., <=0.

An octagon is an eight-sided polygon. Several special types of octagons are illustrated above. In particular, an octagon with vertices equally spaced around a circle and with ...

AW, AB, and AY in the above figure are in a harmonic range.

A pentagon is a five-sided polygon. Several special types of pentagons are illustrated above. In particular, a pentagon with vertices equally spaced around a circle and with ...

A plane partition is a two-dimensional array of integers n_(i,j) that are nonincreasing both from left to right and top to bottom and that add up to a given number n. In ...

The diameter of a polygon is the largest distance between any pair of vertices. In other words, it is the length of the longest polygon diagonal (e.g., straight line segment ...

The definition of a set by enumerating its members. An extensional definition can always be reduced to an intentional one. An extension field is sometimes also called simply ...