Direct decomposability of tolerances on lattices, semilattices and quasilattices
We prove that an order algebra assigned to a bounded poset with involution is a discriminator algebra.
The theory of discriminator algebras and varieties has been investigated extensively, and provides us with a wealth of information and techniques applicable to specific examples of such algebras and varieties. Here we give several such examples for Boolean algebras with a residuated binary operator, abbreviated as r-algebras. More specifically, we show that all finite r-algebras, all integral r-algebras, all unital r-algebras with finitely many elements below the unit, and all commutative residuated...
Some decompositions of general incidence structures with regard to distinguished components (modular or simple) are considered and several structure theorems for them are deduced.
We present a formal scheme which whenever satisfied by relations of a given relational lattice containing only reflexive and transitive relations ensures distributivity of .