Which O-commutative Basic Algebras Are Effect Algebras

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Authors	PASEKA Jan
Year of publication	2010
Type	Article in Periodical
Magazine / Source	International Journal of Theoretical Physics
MU Faculty or unit	Faculty of Science
Citation
Web	http://dx.doi.org/10.1007/s10773-009-0221-9
Field	General mathematics
Keywords	Basic algebra Commutative basic algebra O-commutative basic algebra Lattice effect algebra
Description	By a basic algebra is meant an MV-like algebra (A,+,neg,0) of type (2, 1, 0) derived in a natural way from bounded lattices having antitone involutions on their principal filters. We show that (i) atomic Archimedean basic algebras for which the operation + is o-commutative are effect algebras and (ii) atomic Archimedean commutative basic algebras are MV-algebras. This generalizes the results by Botur and Halas on finite commutative basic algebras and complete commutative basic algebras.
Related projects:	Mathematical structures and their physical applications