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Centralizer

From Encyclopedia of Mathematics - Reading time: 1 min

The subset of a ring, group or semi-group R consisting of elements that commute (are interchangable) with all elements of a certain set XR; the centralizer of S in R is denoted by CR(S). 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).

References[edit]

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

How to Cite This Entry: Centralizer (Encyclopedia of Mathematics) | Licensed under CC BY-SA 3.0. Source: https://encyclopediaofmath.org/wiki/Centralizer
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