Difference between revisions of "Centralizer"
From Encyclopedia of Mathematics
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| − | The subset of a ring, group or semi-group | + | {{TEX|done}} |
| + | 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). | ||
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<table><TR><TD valign="top">[1]</TD> <TD valign="top"> N. Jacobson, "Structure of rings" , Amer. Math. Soc. (1956)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> N. Jacobson, "Structure of rings" , Amer. Math. Soc. (1956)</TD></TR></table> | ||
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Latest revision as of 19:54, 11 April 2014
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
| [1] | N. Jacobson, "Structure of rings" , Amer. Math. Soc. (1956) |
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