caa a22 4500 605469415 CHVBK 20210128100322.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s00500-014-1468-5 doi (NATIONALLICENCE)springer-10.1007/s00500-014-1468-5 Dvurečenskij Anatolij Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia aut On a new construction of pseudo effect algebras [Elektronische Daten] [Anatolij Dvurečenskij] 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. Springer-Verlag Berlin Heidelberg, 2014 Pseudo effect algebra nationallicence Generalized pseudo effect algebra nationallicence Po-group nationallicence Strong unit nationallicence Riesz decomposition property nationallicence Lexicographic product nationallicence Kite pseudo effect algebra nationallicence Normal ideal nationallicence Subdirect irreducibility nationallicence Soft Computing Springer Berlin Heidelberg 19/3(2015-03-01), 517-529 1432-7643 19:3<517 2015 19 500 https://doi.org/10.1007/s00500-014-1468-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-014-1468-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dvurečenskij Anatolij Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/3(2015-03-01), 517-529 1432-7643 19:3<517 2015 19 500