Isomorphism theorems on generalized effect algebras based on atoms

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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.
Related projects:	Mathematical structures and their physical applications