Lattices of two-sided ideals of locally matricial algebras and the Gamma-invariant problem

摘要

We develop a method of representation of distributive (boolean OR,0,1)-semilattices as semilattices of finitely generated ideals of locally matricial algebras. We use the method to reprove two representation results by G. M. Bergman and prove a new one that every distributive (0, 1)-lattice is, as a semilattice, isomorphic to the semilattice of all finitely generated ideals of a locally matricial algebra. We apply this fact to solve the Gamma-invariant problem.