minimal ideal

Definitions

1. 1

   A nonzero (two-sided) ideal that contains no other nonzero two-sided ideal.

   • Of particular interest are the primitive rings with minimal ideals, algebraic algebras and algebras with a polynomial identity.
   • Theorem 12. A semisimple ring R has only a finite number of minimal ideals and is their direct sum. Moreover, each minimal ideal is a simple ring.
   • Note that if a semigroup has a zero, then its minimal ideal is {0}. In this context, the notion of minimal ideal is not so useful, and so we introduce the notion of a 0-minimal ideal.

The neighborhood