Abstract

For a Peirce algebra \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal P}$\end{document}, lattices \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathrm{Cong}\mathcal {P}$\end{document} of all heterogenous Peirce congruences and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathrm{Ide}\mathcal {P}$\end{document} 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 \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathrm{Cong}\mathcal {P}$\end{document} and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathrm{Ide}\mathcal {P}$\end{document}. 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.