Center (ring theory)


In algebra, the centre 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(R); 'Z' stands for the German word Zentrum, meaning "centre".

If R is a ring, then R is an associative algebra over its centre. 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.

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Notes edit

  1. ^ "vector spaces – A linear operator commuting with all such operators is a scalar multiple of the identity". Retrieved 2017-07-22.

References edit

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