Publication details

Which O-commutative Basic Algebras Are Effect Algebras

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.
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