Simple ring: Difference between revisions
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Latest revision as of 16:34, 12 May 2008
Definition
Symbol-free definition
A ring is termed simple if it satisfies the following equivalent conditions:
- It has no proper nontrivial two-sided ideal
- Any homomorphism from it is either trivial or injective
Definition with symbols
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Relation with other properties
Stronger properties
Weaker properties
Metaproperties
Left-right symmetry
The property of being a simple ring is left-right symmetric. That is, a ring is simple if and only if its opposite ring is simple.