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The multiplication operation corresponding to the Lie bracket.

A noncommutative ring R is a ring in which the law of multiplicative commutativity is not satisfied, i.e., a·b!=b·a for any two elements a,b in R. In such a case, the ...

A reduced root system is a root system R satisfying the additional property that, if alpha in R, then the only multiples of alpha in R are +/-alpha.

A semiprime ring which is also an Artinian ring.

In general, there is no unique matrix solution A to the matrix equation y=Ax. Even in the case of y parallel to x, there are still multiple matrices that perform this ...

Let A^~, B^~, ... be operators. Then the commutator of A^~ and B^~ is defined as [A^~,B^~]=A^~B^~-B^~A^~. (1) Let a, b, ... be constants, then identities include [f(x),x] = 0 ...

A module that fulfils the descending chain condition with respect to inclusion, i.e., if every decreasing sequence of submodules eventually become constant.

A ring with a unit element in which every element is idempotent.

The usual type of vector, which can be viewed as a contravariant tensor ("ket") of tensor rank 1. Contravariant vectors are dual to one-forms ("bras," a.k.a. covariant ...

The acceleration of an element of fluid, given by the convective derivative of the velocity v, (Dv)/(Dt)=(partialv)/(partialt)+v·del v, where del is the gradient operator.