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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).


[1] N. Jacobson, "Structure of rings" , Amer. Math. Soc. (1956)


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Centralizer. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by L.A. Bokut (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article