Difference between revisions of "Semi-simple ring"
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| − | A ring $R$ with zero radical. More precisely, if $\mathcal{R}$ is some radical (see [[Radical of rings and algebras|Radical of rings and algebras]]), then the ring $R$ is called $\mathcal{R}$-semi-simple if $\mathcal{R}(R) = 0$. Frequently, by an associative semi-simple ring one understands a [[ | + | A ring $R$ with zero radical. More precisely, if $\mathcal{R}$ is some radical (see [[Radical of rings and algebras|Radical of rings and algebras]]), then the ring $R$ is called $\mathcal{R}$-semi-simple if $\mathcal{R}(R) = 0$. Frequently, by an associative semi-simple ring one understands a [[classical semi-simple ring]]. |
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Revision as of 19:40, 19 October 2014
A ring $R$ with zero radical. More precisely, if $\mathcal{R}$ is some radical (see Radical of rings and algebras), then the ring $R$ is called $\mathcal{R}$-semi-simple if $\mathcal{R}(R) = 0$. 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=33971
Semi-simple ring. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Semi-simple_ring&oldid=33971
This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article