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Let K be a number field, then each fractional ideal I of K belongs to an equivalence class [I] consisting of all fractional ideals J satisfying I=alphaJ for some nonzero ...

An odd prime p is called a cluster prime if every even positive integer less than p-2 can be written as a difference of two primes q-q^', where q,q^'<=p. The first 23 odd ...

Codimension is a term used in a number of algebraic and geometric contexts to indicate the difference between the dimension of certain objects and the dimension of a smaller ...

Two matrices A and B which satisfy AB=BA (1) under matrix multiplication are said to be commuting. In general, matrix multiplication is not commutative. Furthermore, in ...

A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

A partially ordered set (or ordered set or poset for short) (L,<=) is called a complete lattice if every subset M of L has a least upper bound (supremum, supM) and a greatest ...

The complete products of a Boolean algebra of subsets generated by a set {A_k}_(k=1)^p of cardinal number p are the 2^p Boolean functions B_1B_2...B_p=B_1 intersection B_2 ...

A measure which takes values in the complex numbers. The set of complex measures on a measure space X forms a vector space. Note that this is not the case for the more common ...

Let P be the principal (initial investment), r be the annual compounded rate, i^((n)) the "nominal rate," n be the number of times interest is compounded per year (i.e., the ...

Let X and Y be sets, and let R subset= X×Y be a relation on X×Y. Then R is a concurrent relation if and only if for any finite subset F of X, there exists a single element p ...