# Centre of a ring

From Encyclopedia of Mathematics

2020 Mathematics Subject Classification: *Primary:* 08-XX [MSN][ZBL]

The centre of a ring $R$ is
the collection $Z$ of all elements of the ring $R$ that commute with every
element, that is,
$$Z=\{z: az = za \textrm{ for all }a \in R\}.$$
The centre of a ring is a subring containing
together with every invertible element its inverse. The centre of a
ring that is an algebra with a unit element over a field contains the
ground field (see
Central algebra).

**How to Cite This Entry:**

Centre of a ring.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Centre_of_a_ring&oldid=21553

This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article