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The ascending chain condition, commonly abbreviated "A.C.C.," for a partially ordered set X requires that all increasing sequences in X become eventually constant. A module M ...

A block matrix is a matrix that is defined using smaller matrices, called blocks. For example, [A B; C D], (1) where A, B, C, and D are themselves matrices, is a block ...

A generalization of Grassmann coordinates to m-D algebraic varieties of degree d in P^n, where P^n is an n-dimensional projective space. To define the Chow coordinates, take ...

A module having dual properties with respect to a free module, as enumerated below. 1. Every free module is projective; every cofree module is injective. 2. For every module ...

A cyclotomic field Q(zeta) is obtained by adjoining a primitive root of unity zeta, say zeta^n=1, to the rational numbers Q. Since zeta is primitive, zeta^k is also an nth ...

The descending chain condition, commonly abbreviated "D.C.C.," is the dual notion of the ascending chain condition. The descending chain condition for a partially ordered set ...

The direct limit, also called a colimit, of a family of R-modules is the dual notion of an inverse limit and is characterized by the following mapping property. For a ...

A coordinate system defined by the transformation equations x = a/Lambdacnmucnnucospsi (1) y = a/Lambdacnmucnnusinpsi (2) z = a/Lambdasnmudnmusnnudnnu, (3) where ...

Division by zero is the operation of taking the quotient of any number x and 0, i.e., x/0. The uniqueness of division breaks down when dividing by zero, since the product ...

For any alpha in A (where A denotes the set of algebraic numbers), let |alpha|^_ denote the maximum of moduli of all conjugates of alpha. Then a function ...