Publication details

Isomorphism theorems on generalized effect algebras based on atoms

Authors

PASEKA Jan RIEČANOVÁ Zdenka RIEČANOVÁ Zdenka

Year of publication 2009
Type Article in Periodical
Magazine / Source INFORMATION SCIENCES
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords Non-classical logics; D-posets; Effect algebras; MV-algebras; States; Probabilities on quantum structures
Description A well-known fact is that every generalized effect algebra can be uniquely extended to an effect algebra in which it becomes a sub-generalized effect algebra and simultaneously a proper order ideal, the set-theoretic complement of which is its dual poset. We show that two non-isomorphic generalized effect algebras (even finite ones) may have isomorphic effect algebraic extensions. For Archimedean atomic lattice effect algebras we prove "Isomorphism theorem based on atoms". As an application we obtain necessary and sufficient conditions for isomorphism of two prelattice Archimedean atomic generalized effect algebras with common (or isomorphic) effect algebraic extensions.
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