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Given two modules M and N over a unit ring R, Hom_R(M,N) denotes the set of all module homomorphisms from M to N. It is an R-module with respect to the addition of maps, ...

An abstract algebra concerned with results valid for many different kinds of spaces. Modules are the basic tools used in homological algebra.

A hypergeometric series sum_(k)c_k is a series for which c_0=1 and the ratio of consecutive terms is a rational function of the summation index k, i.e., one for which ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

Let S be a mathematical statement, then the Iverson bracket is defined by [S]={0 if S is false; 1 if S is true, (1) and corresponds to the so-called characteristic function. ...

A ket |psi> is a vector living in a dual vector space to that containing bras <psi|. Bras and kets are commonly encountered in quantum mechanics. Bras and kets can be ...

Let phi_x^((k)) denote the recursive function of k variables with Gödel number x, where (1) is normally omitted. Then if g is a partial recursive function, there exists an ...

The most general form of this theorem states that in a commutative unit ring R, the height of every proper ideal I generated by n elements is at most n. Equality is attained ...

The (associated) Legendre function of the first kind P_n^m(z) is the solution to the Legendre differential equation which is regular at the origin. For m,n integers and z ...

The Lemoine cubic is the triangle cubic with trilinear equation It passes through Kimberling centers X_n for n=3, 4, 32, 56, and 1147.