Abstract
By a basic algebra is meant an MV-like algebra (A,⊕,¬,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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