Ivan Chajda (2005)
Discussiones Mathematicae - General Algebra and Applications
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We present a simple condition under which a bounded lattice L with sectionally antitone involutions becomes an MV-algebra. In thiscase, L is distributive. However, we get a criterion characterizingdistributivity of L in terms of antitone involutions only.
Ján Jakubík (2006)
Mathematica Slovaca
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Néstor G. Martínez, Hilary A. Priestley (1995)
Mathware and Soft Computing
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It is shown that the implication of an MV-algebra is determined by de Morgan negation operations on a family of quotients of the given algebra; these quotients may be taken to be totally ordered. Certain existing results on the uniqueness of an MV-algebra implication are thereby elucidated and new criteria for uniqueness derived. These rely on a characterisation of chains on which a de Morgan negation is necessarily unique.
Ivan Chajda, Jan Kühr (2006)
Mathematica Slovaca
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Ivan Chajda (2009)
Mathematica Bohemica
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A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra.