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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 ...

A metric space X which is not complete has a Cauchy sequence which does not converge. The completion of X is obtained by adding the limits to the Cauchy sequences. For ...

Two complex numbers x=a+ib and y=c+id are multiplied as follows: xy = (a+ib)(c+id) (1) = ac+ibc+iad-bd (2) = (ac-bd)+i(ad+bc). (3) In component form, ...

The Dedekind psi-function is defined by the divisor product psi(n)=nproduct_(p|n)(1+1/p), (1) where the product is over the distinct prime factors of n, with the special case ...

The word "degree" has many meanings in mathematics. The most common meaning is the unit of angle measure defined such that an entire rotation is 360 degrees. This unit harks ...

The divergence theorem, more commonly known especially in older literature as Gauss's theorem (e.g., Arfken 1985) and also known as the Gauss-Ostrogradsky theorem, is a ...

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 ...

A module M over a unit ring R is called flat iff the tensor product functor - tensor _RM (or, equivalently, the tensor product functor M tensor _R-) is an exact functor. For ...

If there exists a one-to-one correspondence between two subgroups and subfields such that G(E(G^')) = G^' (1) E(G(E^')) = E^', (2) then E is said to have a Galois theory. A ...

A minimal free resolution of a finitely generated graded module M over a commutative Noetherian Z-graded ring R in which all maps are homogeneous module homomorphisms, i.e., ...