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Endomorphism Ring


Given a module M over a unit ring R, the set End_R(M) of its module endomorphisms is a ring with respect to the addition of maps,

 (f+g)(x)=f(x)+g(x),    for all x in M,

and the product given by map composition,

 (fg)(x)=f degreesg(x)=f(g(x)),    for all x in M.

The endomorphism ring of M is, in general, noncommutative, but it is always a unit ring (its unit element being the identity map on M).


See also

Endomorphism, Schur's Lemma

This entry contributed by Margherita Barile

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Cite this as:

Barile, Margherita. "Endomorphism Ring." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/EndomorphismRing.html

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