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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.

A change of basis is the transformation of coordinate-based vector and operator representations in a given vector space from one vector basis representation to another.

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.

Defined for a vector field A by (A·del ), where del is the gradient operator. Applied in arbitrary orthogonal three-dimensional coordinates to a vector field B, the ...

A covariant tensor of rank 1, more commonly called a one-form (or "bra").

The rotation vector of the trihedron of a curve with curvature kappa!=0 when a point moves along a curve with unit speed. It is given by D=tauT+kappaB, (1) where tau is the ...

The upside-down capital delta symbol del , also called "nabla" used to denote the gradient and other vector derivatives. The following table summarizes the names and ...

For {M_i}_(i in I) a family of R-modules indexed by a directed set I, let sigma_(ij):M_i->M_j i<=j be an R-module homomorphism. Call (M_i,sigma_(ij)) a direct system over I ...