Difference between revisions of "Chain ring"
From Encyclopedia of Mathematics
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| − | A ring (usually assumed to be associative and with a unit element) in which the left ideals form a chain. In other words, | + | A ring (usually assumed to be associative and with a unit element) in which the left ideals form a chain. In other words, $R$ is a left chain ring if $R$ is a left chain module over itself. Every left chain ring is local. Right chain rings are defined similarly. Commutative chain rings are often called normed rings. See also [[Discretely-normed ring|Discretely-normed ring]]. |
Latest revision as of 09:26, 27 April 2014
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A ring (usually assumed to be associative and with a unit element) in which the left ideals form a chain. In other words, $R$ is a left chain ring if $R$ is a left chain module over itself. Every left chain ring is local. Right chain rings are defined similarly. Commutative chain rings are often called normed rings. See also Discretely-normed ring.
How to Cite This Entry:
Chain ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Chain_ring&oldid=31942
Chain ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Chain_ring&oldid=31942
This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article