simple ring
SimpleRing
2001-10-20 02:37:43
2002-10-25 18:10:59
Definition
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A nonzero ring $R$ is said to be a {\it simple ring} if it has no (two-sided) ideal other then the zero ideal and $R$ itself.
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This is equivalent to saying that the zero ideal is a maximal ideal.
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If $R$ is a commutative ring with unit, then this is equivalent to being a field.