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Unitizing a Generalized Pseudo Effect Algebra
Order, 2014It is known that every generalized effect algebra can be embedded as a maximal proper ideal in an effect algebra called its unitization. Here this result is extended to the non-commutative case of \textit{pseudo effect algebras}. Necessary and sufficient conditions are found for a generalized pseudo effect algebra to admit a unitization.
Sylvai Pulmannova, David J. Foulis
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Generalized homogeneous, prelattice and MV-effect algebras. [PDF]
Kybernetika, 2005 Summary: We study unbounded versions of effect algebras. We show a necessary and sufficient condition for lattice operations of such a generalized effect algebra \(P\) to be inherited under its embeding as a proper ideal with a special property and closed under the effect sum into an effect algebra.
Zdenka Riecanová, Ivica Marinová
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Embeddings of generalized effect algebras into complete effect algebras
Soft Computing, 2005The author studies unbounded effect algebras. It is shown that under some condition, Archime\-de\-anicity or block finiteness, the MacNeille completion can be densely embedded into a complete effect algebra.
Borzooei, Rajab Ali +2 more
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Algebraic Operations and Generic Effects
Applied Categorical Structures, 2003\textit{E. Moggi} [in: Proc. LICS '89, IEEE Press, 14-23 and Inf. Comput. 93, 55-92 (1991; Zbl 0723.68073)] introduced the idea of giving a unified category-theoretic semantics for computational effects, modeling each of them in the Kleisli category of an appropriate strong monad on a base category with finite products. However, the calculus of Moggi's
Gordon D. Plotkin, John Power
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Intervals in generalized effect algebras
Soft Computing, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jirí Janda, Zdenka Riecanová
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The Exocenter of a Generalized Effect Algebra
Reports on Mathematical Physics, 2011A generalized effect algebra is obtained from an effect algebra if we do not require the existence of the greatest element. Conversely, it can be canonically embedded into an effect algebra by the procedure of unitization. The exocenter is a collection of mappings which, in effect algebras, correspond to projections on central ideals (equivalently, on ...
Foulis, David J., Pulmannová, Sylvia
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Generalized pseudo-EMV-effect algebras
Soft Computing, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anatolij Dvurecenskij, Omid Zahiri
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A non-associative generalization of effect algebras
Soft Computing, 2012The authors introduce the so-called skew effect algebras as non-associative generalizations of effect algebras. They show that every skew effect algebra is a bounded poset with an antitone involution and that there is a one-to-one correspondence between skew effect algebras and special bounded posets with sectionally switching involutions (SSI-posets).
Ivan Chajda, Helmut Länger
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Associativity and Distributivity-Like Properties in Generalized Effect Algebras
International Journal of Theoretical Physics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Josef Tkadlec, Petr Žáček
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On the Structure of Generalized Effect Algebras and Separation Algebras
2018Separation algebras are models of separation logic and effect algebras are models of unsharp quantum logics. We investigate these closely related classes of partial algebras as well as their noncommutative versions and the subclasses of (generalized) (pseudo-)orthoalgebras.
Sarah Alexander +2 more
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