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In this article, it will be shown that every -subgroup of a Specker -group has singular elements and that the class of -groups that are -subgroups of Specker -group form a torsion class. Methods of adjoining units and bases to Specker -groups are then studied with respect to the generalized Boolean algebra of singular elements, as is the strongly projectable hull of a Specker -group.
We present very short and simple proofs of such facts as co-frame distributivity of sublocales, zero-dimensionality of the resulting co-frames, Isbell’s Density Theorem and characteristic properties of fit and subfit frames, using sublocale sets.
In this note we show that a subtraction algebra is equivalent to an implicative -algebra, and a subtraction semigroup is a special case of a -semigroup.
A subtraction semigroup is a semigroup with a further operation "" added, called subtraction and satisfying certain axioms. The paper concerns a problem by B. M. Schein concerning the structure of multiplication in a subtraction semigroup.
A De Morgan quasilattice is an algebra satisfying hyperidentities of the variety of De Morgan algebras (lattices). In this paper we give a functional representation of the free n-generated De Morgan quasilattice with two binary and one unary operations. Namely, we define the concept of super-De Morgan function and prove that the free De Morgan quasilattice with two binary and one unary operations on nfree generators is isomorphic to the De Morgan quasilattice of super-De Morgan functions of nvariables....
In a former paper, motivated by a recent theory of relators (families of relations), we have investigated increasingly regular and normal functions of one preordered set into another instead of Galois connections and residuated mappings of partially ordered sets. A function of one preordered set into another has been called (1) increasingly -normal, for some function of into , if for any and we have if and only if ; (2) increasingly -regular, for some function of into itself,...