Center (algebra)
Revision as of 11:15, 11 May 2008 by Boy Soprano II (talk | contribs) (New page: In general, the '''center''' of an algebraic structure is the set of elements which commute with every of the structure. With groups, this definition is straightforward; for rings...)
In general, the center of an algebraic structure is the set of elements which commute with every of the structure. With groups, this definition is straightforward; for rings and fields, the commutativity in question is multiplicative commutativity.
The center of a group is never empty, as the identity commutes with every element of a group. The center of a group is a subgroup of the group—a normal subgroup, in fact; it is also stable under any endomorphism on the group.
See also
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