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An Abelian category is a category for which the constructions and techniques of homological algebra are available. The basic examples of such categories are the category of ...

The Jacobian conjecture in the plane, first stated by Keller (1939), states that given a ring map F of C[x,y] (the polynomial ring in two variables over the complex numbers ...

Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

A two-sided (doubly infinite) Z-Transform, Z^((2))[{a_n}_(n=-infty)^infty](z)=sum_(n=-infty)^infty(a_n)/(z^n) (Zwillinger 1996; Krantz 1999, p. 214). The bilateral transform ...

A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal ...

The Hilbert transform (and its inverse) are the integral transform g(y) = H[f(x)]=1/piPVint_(-infty)^infty(f(x)dx)/(x-y) (1) f(x) = ...

The ramp function is defined by R(x) = xH(x) (1) = int_(-infty)^xH(x^')dx^' (2) = int_(-infty)^inftyH(x^')H(x-x^')dx^' (3) = H(x)*H(x), (4) where H(x) is the Heaviside step ...

Let A be a commutative ring and let C_r be an R-module for r=0,1,2,.... A chain complex C__ of the form C__:...|->C_n|->C_(n-1)|->C_(n-2)|->...|->C_2|->C_1|->C_0 is said to ...

The term endomorphism derives from the Greek adverb endon ("inside") and morphosis ("to form" or "to shape"). In algebra, an endomorphism of a group, module, ring, vector ...

Given a field F and an extension field K superset= F, if alpha in K is an algebraic element over F, the minimal polynomial of alpha over F is the unique monic irreducible ...