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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.

The sum of the reciprocals of roots of an equation equals the negative coefficient of the linear term in the Maclaurin series.

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 ...

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^*. ...

Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y. (2) Now define Z={x in A:x·y=0 for some y in A!=0}, (3) where 0 in Z. An Associative ...

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 Lie algebra is nilpotent when its Lie algebra lower central series g_k vanishes for some k. Any nilpotent Lie algebra is also solvable. The basic example of a nilpotent Lie ...