Abstract
A noncommutative version of generalized Sasaki projections in pseudoeffect algebras is introduced. It is proved that an ideal in a pseudoeffect algebra is Riesz if and only if it is closed under the right and left Sasaki projections. In lattice ordered pseudoeffect algebras, it is shown that generalized Sasaki projections are one-element sets, and their explicit form is found. It is shown that if a supremum of a normal Riesz ideal in a lattice ordered pseudoeffect algebra exists, it is a central element. These results extend those obtained recently by Avallone and Vitolo for effect algebras.
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Pulmannová, S. Generalized Sasaki Projections and Riesz Ideals in Pseudoeffect Algebras. International Journal of Theoretical Physics 42, 1413–1423 (2003). https://doi.org/10.1023/A:1025723811099
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DOI: https://doi.org/10.1023/A:1025723811099