Difference between revisions of "Centre of a ring"
From Encyclopedia of Mathematics
Ulf Rehmann (talk | contribs) m (tex,msc) |
Ulf Rehmann (talk | contribs) m (typo) |
||
| Line 1: | Line 1: | ||
| + | {{MSC|08}} | ||
{{TEX|done}} | {{TEX|done}} | ||
| − | + | ||
The centre of a ring $R$ is | The centre of a ring $R$ is | ||
Latest revision as of 21:43, 5 March 2012
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=21372
Centre of a ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Centre_of_a_ring&oldid=21372
This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article