endomorphism

An endomorphism is a homomorphism from an object to itself.

It is called the endomorphism ring of the module V.

The endomorphism ring is simply the ring of formal power series.

The endomorphism ring encodes several internal properties of the object.

Let be a probability space, and a measure-preserving endomorphism of .

Any ring with unity is the endomorphism ring of some object.

The characteristic polynomial of this endomorphism has the following form:

The endomorphism maps every element to its pth power.

Otherwise φ is an endomorphism but not a ring automorphism.

In particular, the endomorphism ring of a simple module is a division ring.

During this period he worked on Abelian varieties and their endomorphism algebras.

A map is a lift of the Frobenius endomorphism provided .

The endomorphism ring is the ring we need for the category of R-modules.

More generally, endomorphism rings of abelian groups are rarely commutative.

The operation of string projection is an endomorphism.

An invertible endomorphism of X is called an automorphism.

Every endomorphism of M is either nilpotent or invertible.

The linear transformation is also called the curvature transformation or endomorphism.

Any such complex torus has the Gaussian integers as endomorphism ring.

A more formal treatment and definition of the structure constants are given in the article on the adjoint endomorphism.

Every indecomposable algebraically compact module has a local endomorphism ring.

Closure: composition of two endomorphisms is another endomorphism.

The endomorphism ring of an Artinian uniform module is a local ring.

The Frobenius endomorphism of over extends to the elliptic curve by .

The endomorphism ring is a semiprimitive ring (that is, ).