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Centre of a ring

From Encyclopedia of Mathematics
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2010 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://www.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