In abstract algebra, the endomorphism ring of an abelian group X, denoted by End(X), is the set of all homomorphisms of X into itself. The addition operation is defined by pointwise addition of functions and the multiplication operation is defined by function composition.
The type of functions involved can change depending upon the category of the Abelian group under examination. The endomorphism ring encodes several internal properties of the object. As the resulting object is often an algebra over some ring R, this may also be called the endomorphism algebra.
Read more about Endomorphism Ring: Description, Examples, Properties
Famous quotes containing the word ring:
“But whatever happens, wherever the scene is laid, somebody, somewhere, will quietly set out—somebody has already set out, somebody still rather far away is buying a ticket, is boarding a bus, a ship, a plane, has landed, is walking toward a million photographers, and presently he will ring at my door—a bigger, more respectable, more competent Gradus.”
—Vladimir Nabokov (1899–1977)