Reflexive Homomorphic Relations
George D. Findlay · Canadian Mathematical Bulletin · 1960
It is well known that a symmetric and transitive relation on a set is reflexive wherever it is defined. In this note we show that a converse is true for homomorphic relations in certain classes of algebras. Consider a class of similar algebras which contains the sub-algebras and quotient algebras of each of its members. Assume also that the direct product A x B of each pair A, B in is also an algebra belonging to . The algebras of , being similar, have the same set of operations. We observe that other operations, called compound operations, may be obtained by composition from the assigned operations.