Publication details
Isomorphism theorems on generalized effect algebras based on atoms
| Authors | |
|---|---|
| Year of publication | 2009 |
| Type | Article in Periodical |
| Magazine / Source | INFORMATION SCIENCES |
| MU Faculty or unit | |
| 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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