nLab
simple ring

A ring RR is simple if it is it is a simple object in the category of RR-RR-bimodules.

This can be stated in more elementary terms in any of the following equivalent ways:

  • RR is nontrivial and has no nontrivial two-sided ideals.
  • RR has exactly two two-sided ideals (which must be RR itself and its zero ideal).

In constructive algebra, this is too strong; we must say:

  • For each two-sided ideal II, II is the zero ideal if and only if II is proper (not equal to RR).
Revised on November 27, 2009 17:06:30 by Toby Bartels (173.60.119.197)