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Title: Congruences and ideals on Boolean modules: a heterogeneous point of view
Authors: Pinto, Sandra Marques 
Oliveira-Martins, M. Teresa 
Keywords: Relation algebras; Boolean modules; Modular heterogeneous congruence; Modular heterogeneous ideal; Simple Boolean module
Issue Date: 2010
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 10-27 (2010)
Serial title, monograph or event: Pré-Publicações DMUC
Issue: 10-27
Place of publication or event: Coimbra
Abstract: Definitions for heterogeneous congruences and heterogeneous ideals on a Boolean module M are given and the respective lattices CongM and IdeM are presented. A characterization of the simple 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 CongM and IdeM. This isomorphism leads us to conclude that the class of the Boolean module is ideal determined.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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