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01-03-2015 | Foundations

On a new construction of pseudo effect algebras

Author: Anatolij Dvurečenskij

Published in: Soft Computing | Issue 3/2015

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Abstract

We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which are connected not necessarily with partially ordered groups, but rather with generalized pseudo effect algebras where the greatest element is not guaranteed. Starting even with a commutative generalized pseudo effect algebra, we can obtain a non-commutative pseudo effect algebra. We show how such kite pseudo effect algebras are tied with different types of the Riesz decomposition properties. We find conditions when kite pseudo effect algebras have the least non-trivial normal ideal.

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Title: On a new construction of pseudo effect algebras
Author: Anatolij Dvurečenskij
Publication date: 01-03-2015
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 3/2015
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-014-1468-5

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