Difference between revisions of "Semi-simple ring"
From Encyclopedia of Mathematics
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| − | A ring $ | + | A ring $A$ with zero radical. More precisely, if $\mathcal{R}$ is some radical (see [[Radical of rings and algebras]]), then the ring $A$ is called $\mathcal{R}$-semi-simple if $\mathcal{R}(A) = 0$. Frequently, by an associative semi-simple ring one understands a [[classical semi-simple ring]]. |
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[[Category:Associative rings and algebras]] | [[Category:Associative rings and algebras]] | ||
Latest revision as of 19:41, 19 October 2014
A ring $A$ with zero radical. More precisely, if $\mathcal{R}$ is some radical (see Radical of rings and algebras), then the ring $A$ is called $\mathcal{R}$-semi-simple if $\mathcal{R}(A) = 0$. Frequently, by an associative semi-simple ring one understands a classical semi-simple ring.
How to Cite This Entry:
Semi-simple ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Semi-simple_ring&oldid=33972
Semi-simple ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Semi-simple_ring&oldid=33972
This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article