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3 Demonstratio Mathematica

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Mv-like algebras associated to lambda-ortholattices

Chajda I., Emanovsky P., Kolarik M.

Demonstratio Mathematica

2007

Vol. 40, nr 2

261-270

The concept of a ambda-lattice generalizes a lattice by substituting associativity by the so-called skew associativity. When a bounded ambda-lattice is equipped with a monotonous unary involution which is a complementation, it is called a ambda-ortholattice. For ambda-ortholattices a Sheffer operation is constructed and, moreover, a derived algebra analogous to an MV-algebra is assigned whenever the ambda-lattice has antitone involutions on sections.

A common generalization of ortholattices and Boolean quasirings

Chajda I., Langer H.

Demonstratio Mathematica

2007

Vol. 40, nr 4

769-774

In [2] a common generalization of Boolean algebras and Boolean rings was introduced. In a similar way we introduce a common generalization of ortholattices and Boolean quasirings.

Modifications of MV-algebras corresponding to strong ortholattices

Chajda I., Länger H.

Demonstratio Mathematica

2005

Vol. 38, nr 1

1--6

It is well-known that principal filters of MV-algebras are de Morgan algebras with involutory complementation. A modification of the notion of an MV-algebra is presented having the property that all principal filters are ortholattices. It turns out that the commutativity of these modified MV-algebras is equivalent to the distributivity of the corresponding ortholattices.