Pulmannová, S.; Vinceková, E. Riesz ideals in generalized effect algebras and in their unitizations. (English) Zbl 1139.81007 Algebra Univers. 57, No. 4, 393-417 (2007). The authors study congruences and ideals of generalized effect algebras, generalized orthoalgebras, weak generalized orthomodular posets, generalized orthomodular lattices, and generalized MV-algebras. Here “generalized” means that the poset does not have an upper bound; this can be always added by the canonical contruction of unitization. Any Riesz ideal induces a congruence, but the reverse implication does not hold. When any of the above structures is factorized over a Riesz ideal, we obtain a structure from the same class. Only for generalized orthomodular posets such a result is not known. The relations between Riesz ideals of generalized effect algebras and their unitizations are studied. Also illustrative examples are of special interest. Reviewer: Mirko Navara (Praha) Cited in 1 ReviewCited in 13 Documents MSC: 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) 06C15 Complemented lattices, orthocomplemented lattices and posets 08A55 Partial algebras Keywords:effect algebra; generalized effect algebra; partial aoeiian monoid; Riesz ideal; unitization; generalized orthoalgebra; weak generalized orthomodular poset; generalized orthomodular lattice; generalized MV-algebra; congruence; p-ideal PDFBibTeX XMLCite \textit{S. Pulmannová} and \textit{E. Vinceková}, Algebra Univers. 57, No. 4, 393--417 (2007; Zbl 1139.81007) Full Text: DOI