Equational characterization for two-valued states in OML-lattices and Baer * semigroups

FREYTES H

Cagliari

Congreso; Int. Quantum Structure (IQSA-2012 ); 2012

University of Cagliari

Recently, several authors have paid attention to the study of states over extended algebraic structures, directly or indirectly related to quantum mechanics, as orthomodular posets , MV -algebras  or effect algebras . Common open problems of these structures are the characterization of classes of algebras admitting some special types of states  and the internalization in an algebraic structure of the concept of state. The aim of this work is to investigate and equationally characterize classes of two-valued states  acting over orthomodular lattices and Baer-semigroups. To do this, we enlarge the language of the orthomodular lattices and Baer-semigroups with a unary operator s, satisfying a set of equations, that captures the common properties of several classes of two-valued states.MV -algebras  or effect algebras . Common open problems of these structures are the characterization of classes of algebras admitting some special types of states  and the internalization in an algebraic structure of the concept of state. The aim of this work is to investigate and equationally characterize classes of two-valued states  acting over orthomodular lattices and Baer-semigroups. To do this, we enlarge the language of the orthomodular lattices and Baer-semigroups with a unary operator s, satisfying a set of equations, that captures the common properties of several classes of two-valued states.