Boolean Lattices With Sectional Switching Mappings

Consider a Boolean lattice with a greatest element 1. An interval for (1,,L,LW43;W44;= ) []1a,LaW12; is called a section. In each Section an antitone bijection is defined. We characterize these Lattices by means of two induced binary operations providing that the resulting algebras from a variety. A mapping f, of on to itself is called a switching mapping if and for. We have If for [1a, ] []1a,()()a1f1,af==[]1xa,1a,xX00;X00;W12;()1xfaX00;X00;qpL,qp,X04;W12; the mapping on the section is determined by that of [ , [1] it is shown that the compatibility condition is satisfied . We have got conditions for antitone of switching mapping and a connections with complementation in sections is shown.