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:
“Full fathom five thy father lies,
Of his bones are coral made;
Those are pearls that were his eyes;
Nothing of him that doth fade,
But doth suffer a sea-change
Into something rich and strange.
Sea-nymphs hourly ring his knell:
Ding-dong.
Hark! Now I hear them—ding-dong bell.”
—William Shakespeare (1564–1616)