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Title: Congruences and ideals on Peirce algebras: a heterogeneous/homogeneous point of view
Authors: Pinto, Sandra Marques 
Oliveira-Martins, M. Teresa 
Keywords: Relation algebras; Boolean modules; Peirce algebras; Peirce heterogeneous congruence; Peirce heterogeneous ideal; Simple Peirce algebras
Issue Date: 2010
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 10-28 (2010)
Serial title, monograph or event: Pré-Publicações DMUC
Issue: 10-28
Place of publication or event: Coimbra
Abstract: For a Peirce algebra P, lattices CongP of all heterogenous Peirce congruences and IdeP of all heterogenous Peirce ideals are presented. The notions of kernel of a Peirce congruence and the congruence induced by a Peirce ideal are introduced to describe an isomorphism between CongP and IdeP. This isomorphism leads us to conclude that the class of the Peirce algebras is ideal determined. Opposed to Boolean modules case, each part of a Peirce ideal I = (I1; I2) determines the other one. A similar result is valid to Peirce congruences. A characterization of the simple Peirce algebras is presented coinciding to that given by Brink, Britz and Schmidt in a homogeneous approach.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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