The subset of a ring, group or semi-group consisting of elements that commute (are interchangable) with all elements of a certain set ; the centralizer of in is denoted by . The centralizer of an irreducible subring (that is, one not stabilizing proper subgroups) of endomorphisms of an Abelian group in the ring of all endomorphisms of this group is a division ring (Schur's lemma).
|||N. Jacobson, "Structure of rings" , Amer. Math. Soc. (1956)|
Centralizer. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Centralizer&oldid=16843