Complete Commutative Basic Algebras |
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Authors: | Michal Botur Radomír Halaš |
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Institution: | (1) Department of Algebra and Geometry, Palacky University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic |
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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. In the previous paper (Botur and Hala?, Mult. Valued Log. Soft Comp., 2007) we have shown that finite basic algebras for which the operation ⊕ is commutative are MV-algebras. In this paper we generalize this result by considering commutative basic algebras for which the underlying lattice is complete. |
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Keywords: | Lattice Section antitone involution MV-algebra Basic algebra Residuated groupoid |
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