ON THE SEMIPRIME IDEAL LATTICE OF A RIGHT INVARIANT RING

Abstract

Let R be a right invariant ring and let S(R) be the lattice of all semiprime ideals of R. Let κ be an infinite cardinal. It is proved that S(R) is an algebraic lattice in which the κ-compact elements constitute a sublattice. It follows that S(R) is isomorphic to the congruence lattice of a lattice.

1980 Mathematics Subject Classification (1985 Revision):

• Primary: 16A15
• Secondary: 06B10
• 13F99
• 16A12
• 16A14