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

A left Hilbert Algebra A whose involution is an antilinear isometry is called a unimodular Hilbert algebra. The involution is usually denoted xi|->xi^*.

A division algebra, also called a "division ring" or "skew field," is a ring in which every nonzero element has a multiplicative inverse, but multiplication is not ...

A local Banach algebra is a normed algebra A=(A,|·|_A) which satisfies the following properties: 1. If x in A and f is an analytic function on a neighborhood of the spectrum ...

If A is a graded module and there exists a degree-preserving linear map phi:A tensor A->A, then (A,phi) is called a graded algebra. Cohomology is a graded algebra. In ...

The roots of a semisimple Lie algebra g are the Lie algebra weights occurring in its adjoint representation. The set of roots form the root system, and are completely ...

A function which is not an algebraic function. In other words, a function which "transcends," i.e., cannot be expressed in terms of, algebra. Examples of transcendental ...

The term "transition matrix" is used in a number of different contexts in mathematics. In linear algebra, it is sometimes used to mean a change of coordinates matrix. In the ...

A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a field is ...

A grand unified theory of mathematics which includes the search for a generalization of Artin reciprocity (known as Langlands reciprocity) to non-Abelian Galois extensions of ...