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A differential ideal is an ideal I in the ring of smooth forms on a manifold M. That is, it is closed under addition, scalar multiplication, and wedge product with an ...

A module having only one element: the singleton set {*}. It is a module over any ring R with respect to the multiplication defined by a*=* (1) for every a in R, and the ...

An integral transform which is often written as an ordinary Laplace transform involving the delta function. The Laplace transform and Dirichlet series are special cases of ...

An orthogonal coordinate system is a system of curvilinear coordinates in which each family of surfaces intersects the others at right angles. Orthogonal coordinates ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

Given a ring R with identity, the general linear group GL_n(R) is the group of n×n invertible matrices with elements in R. The general linear group GL_n(q) is the set of n×n ...

Let R be a commutative ring. A tensor category (C, tensor ,I,a,r,l) is said to be a tensor R-category if C is an R-category and if the tensor product functor is an R-bilinear ...

A nonzero module M over a ring R whose only submodules are the module itself and the zero module. It is also called a simple module, and in fact this is the name more ...

The most general form of this theorem states that in a commutative unit ring R, the height of every proper ideal I generated by n elements is at most n. Equality is attained ...

There are at least two distinct notions known as the Whitehead group. Given an associative ring A with unit, the Whitehead group associated to A is the commutative quotient ...