Center (ring theory)

Summary

In algebra, the center of a ring R is the subring consisting of the elements x such that xy = yx for all elements y in R. It is a commutative ring and is denoted as ; "Z" stands for the German word Zentrum, meaning "center".

If R is a ring, then R is an associative algebra over its center. Conversely, if R is an associative algebra over a commutative subring S, then S is a subring of the center of R, and if S happens to be the center of R, then the algebra R is called a central algebra.

ExamplesEdit

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NotesEdit

  1. ^ "vector spaces - A linear operator commuting with all such operators is a scalar multiple of the identity. - Mathematics Stack Exchange". Math.stackexchange.com. Retrieved July 22, 2017.

ReferencesEdit

  • Bourbaki, Algebra.
  • Richard S. Pierce. Associative algebras. Graduate texts in mathematics, Vol. 88, Springer-Verlag, 1982, ISBN 978-0-387-90693-5