Simple ring

From Commalg

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.