MODIFICATIONS OF MV-ALGEBRAS CORRESPONDING TO STRONG ORTHOLATTICES

Abstract

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.DEFINITION 2.1.An MV-algebra is an algebra (A, ->, 0) of type (2,1,0) satisfying