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Embeddings of generalized effect algebras into complete effect algebras

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Abstract

Generalized effect algebras as posets are unbounded versions of effect algebras having bounded effect-algebraic extensions. We show that when the MacNeille completion MC(P) of a generalized effect algebra P cannot be organized into a complete effect algebra by extending the operation ⊕ onto MC(P) then still P may be densely embedded into a complete effect algebra. Namely, we show these facts for Archimedean GMV-effect algebras and block-finite prelattice generalized effect algebras. Moreover, we show that extendable commutative BCK-algebras directed upwards are equivalent to generalized MV-effect algebras.

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  1. Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, 812 19, Bratislava 1, Slovak Republic

    Z. Riečanová

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  1. Z. Riečanová
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Correspondence to Z. Riečanová.

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Riečanová, Z. Embeddings of generalized effect algebras into complete effect algebras. Soft Comput 10, 476–482 (2006). https://doi.org/10.1007/s00500-005-0521-9

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