Studies of various algebraic structures which can be defined over a Boolean algebra by means of Boolean operations have been made by Bernstein [1, 2], Cunkle [3], Elliott [4], Frink [6, 7], Grätzer [8], Grätzer and Schmidt [9], Rudeanu [10, 11], Vaidyanathaswamy [12], Wiener [13], and others. The first determination of all ring structures was made by Frink [7] in 1928. The subclass of Boolean rings has been investigated independently by Grätzer and Schmidt [9], Rudeanu [10, 11], and Gratzer [8]. The investigation of these topics is summarized and completed here, the principal new contributions covering homomorphisms and isomorphisms between the rings.