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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 ...

There are no fewer than three distinct notions of the term local C^*-algebra used throughout functional analysis. A normed algebra A=(A,|·|_A) is said to be a local ...

The Banach space L^1([0,1]) with the product (fg)(x)=int_0^xf(x-y)g(y)dy is a non-unital commutative Banach algebra. This algebra is called the Volterra algebra.

Let P be a class of (universal) algebras. Then an algebra A is a local P-algebra provided that every finitely generated subalgebra F of A is a member of the class P. Note ...

An algebra, also called a nilalgebra, consisting only of nilpotent Elements.

Computer algebra is a diffuse branch of mathematics done with computers that encompasses both computational algebra and analysis.

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

An involutive algebra is an algebra A together with a map a|->a^* of A into A (a so-called involution), satisfying the following properties: 1. (a^*)^*=a. 2. (ab)^*=b^*a^*. ...

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 ...

Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these ...