Locally order affine complete modular lattices of finite height.
by
Vladimir Kuchmei
Institute of Pure Mathematics, University of Tartu, Tartu, Estonia
Coauthors: Kalle Kaarli (Institute of Pure Mathematics, University of Tartu)

A lattice L is called (locally) order affine complete, if all order and congruence preserving functions on L are (local) polynomial functions of that lattice.

The following result was proved by R. Wille for finite case and generalized by K. Kaarli and A. F. Pixley to lattices of finite height.

Theorem A lattice L of finite height is locally order affine complete iff every finitely generated tolerance of L is congruence generated.

It was also proved by K. Kaarli that the characterization of locally order affine complete lattices of finite height can be reduced to subdirect products of two SI lattices.

In view of these results we study tolerances of subdirect products of two finite SI lattices and characterize locally order affine complete modular lattices of finite height.

Date received: May 20, 2004