Centralizer
From Encyclopedia of Mathematics
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).
References
| [1] | N. Jacobson, "Structure of rings" , Amer. Math. Soc. (1956) |
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How to Cite This Entry:
Centralizer. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Centralizer&oldid=16843
Centralizer. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Centralizer&oldid=16843
This article was adapted from an original article by L.A. Bokut (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article