Difference between revisions of "Centre of a ring"
From Encyclopedia of Mathematics
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| − | 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|Central algebra]]). | + | 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|Central algebra]]). | ||
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=18869
Centre of a ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Centre_of_a_ring&oldid=18869
This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article