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 $X\subseteq R$; the centralizer of $S$ in $R$ is denoted by $C_R(S)$. 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/Centralizer2 views | ↧ Download this article as ZWI file
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