Centre of a ring
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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
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