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:
“I was exceedingly interested by this phenomenon, and already felt paid for my journey. It could hardly have thrilled me more if it had taken the form of letters, or of the human face. If I had met with this ring of light while groping in this forest alone, away from any fire, I should have been still more surprised. I little thought that there was such a light shining in the darkness of the wilderness for me.”
—Henry David Thoreau (18171862)