Congruences and ideals on Peirce algebras: a heterogeneous/homogeneous point of view

摘要

For a Peirce algebra P, lattices CongP of all heterogenous Peirce congruencesand IdeP of all heterogenous Peirce ideals are presented. The notions ofkernel of a Peirce congruence and the congruence induced by a Peirce ideal are introducedto describe an isomorphism between CongP and IdeP. This isomorphismleads us to conclude that the class of the Peirce algebras is ideal determined. Opposedto Boolean modules case, each part of a Peirce ideal I = (I1; I2) determines theother one. A similar result is valid to Peirce congruences. A characterization ofthe simple Peirce algebras is presented coinciding to that given by Brink, Britz andSchmidt in a homogeneous approach.