1. Lexicographic pseudo effect algebras.
- Author
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Dvurečenskij, Anatolij
- Subjects
- *
LEXICOGRAPHICAL errors , *EFFECT algebras , *RIESZ spaces , *ASSOCIATIVE algebras , *PSEUDONOISE sequences (Digital communications) , *PSEUDOCODE (Computer program language) - Abstract
We characterize effect algebras and pseudo effect algebras that can be represented as an interval of the lexicographic product of an antilattice unital po-group ( H, u) with a directed po-group G, both with the Riesz Decomposition Property (RDP). We show that a crucial condition is the existence of a lexicographic normal ideal. Finally, we present a categorical equivalence of the category of ( H, u)-lexicographic pseudo effect algebras having RDP with the category of directed po-groups with RDP. In addition, a weaker form of the ( H, u)-lexicographic pseudo effect algebra is studied. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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