Abstract

Definitions for heterogeneous congruences and heterogeneous ideals on a Boolean module equation image are given and the respective lattices equation image and equation image are presented. A characterization of the simple bijective Boolean modules is achieved differing from that given by Brink in a homogeneous approach. We construct the smallest and the greatest modular congruence having the same Boolean part. The same is established for modular ideals. The notions of kernel of a modular congruence and the congruence induced by a modular ideal are introduced to describe an isomorphism between equation image and equation image. This isomorphism leads us to conclude that the class of the Boolean module is ideal determined.