Algebraic distributive lettices, dimension groups and von Neumann regular rings
by
Pavel Ruzicka
Charles University

Rings are assumed to be associative and have a nonzero identity element. If a ring R is von Neumann regular, then the lattice L₂(R) of two-sided ideals of R is algebraic and distributive. We will give a list of results conserning the oposit question whether an algebraic distributive lattice is isomorphic to L₂(R) of some von Neumann regular ring.

We will study the problem restricting our attention to locally matricial algebras, i.e. direct limits of matricial algebras. In this case we will mention the related question, which algebraic distributive lattices are realized as lattices of convex directed subgroups of dimension groups.

Date received: May 24, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caee-67.