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Which O-commutative Basic Algebras Are Effect Algebras

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PASEKA Jan

Rok publikování 2010
Druh Článek v odborném periodiku
Časopis / Zdroj International Journal of Theoretical Physics
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www http://dx.doi.org/10.1007/s10773-009-0221-9
Obor Obecná matematika
Klíčová slova Basic algebra Commutative basic algebra O-commutative basic algebra Lattice effect algebra
Popis 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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