The aim of the paper is to show that if S(G) is distributive, and also G satisfies some additional condition, then the union of any two subgroupoids of G is also a subgroupoid (intuitively, G has to be in some sense a unary algebra).
Let be an infinite cardinal. In this paper we define an interpolation rule for lattice ordered groups. We denote by the class of all lattice ordered groups satisfying , and prove that is a radical class.
In this paper the classes of De Morgan algebras (P(X),∩,U,n) are studied. With respect to isomorphisms of such algebras, being P(X) the fuzzy sets on a universe X taking values in [0,1], U and ∩ the usual union and intersection given by max and min operations and n a proper complement.
Let be an infinite cardinal. We denote by the collection of all -representable Boolean algebras. Further, let be the collection of all generalized Boolean algebras such that for each , the interval of belongs to . In this paper we prove that is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered groups and generalized -algebras.