Riesz ideals in generalized effect algebras and in their unitizations

• Autores: Sylvia Pulmannová, Elena Vinceková
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 57, Nº. 4, 2007, págs. 393-417
• Idioma: inglés
• DOI: 10.1007/s00012-007-2043-z
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• Resumen

  • We show that quotients of generalized effect algebras by Riesz ideals preserve some important special properties, e.g., homogeneity and hereditary Riesz decomposition properties; moreover, quotients of generalized orthoalgebras, weak generalized orthomodular posets, generalized orthomodular lattices and generalized MV-algebras with respect to Riesz ideals belong to the same class. We give a necessary and sufficient condition under which a Riesz ideal I of a generalized effect algebra P is a Riesz ideal also in the unitization E of P. We also study relations between Riesz ideals and central elements in GEAs and in their unitizations. In the last section, we demonstrate the notion of Riesz ideals by some illustrative examples.