endomorphism ring

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.

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

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

In general, endomorphism rings can be defined for the objects of any preadditive category.

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

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

Endomorphism rings and direct sum decompositions in some classes of modules.

Every indecomposable algebraically compact module has a local endomorphism ring.

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

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

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

Under this addition, the endomorphisms of an abelian group form a ring (the endomorphism ring).

As an immediate consequence, we see that the endomorphism ring of every finite-length indecomposable module is local.

The procedure for matrix multiplication can be traced back to compositions of endomorphisms in this endomorphism ring.

The endomorphism ring of a module with finite composition length is a semiprimary ring.

A polarisation induces a Rosati involution on the endomorphism ring of A.

A module is said to be strongly indecomposable if its endomorphism ring is a local ring.

Square matrix rings arise as endomorphism rings of free modules with finite rank.

For a semisimple module, the endomorphism ring is a von Neumann regular ring.

The endomorphism ring of a continuous module or discrete module is a clean ring.

A module of finite length is indecomposable if and only if its endomorphism ring is local.

Endomorphism rings are typically non-commutative.

The endomorphism ring of a nonzero right uniserial module has either one or two maximal right ideals.