A representation of generalized Boolean rings

Topological representation of algebras

“…The next corollary generalizes Stone's topological representation of Boolean rings, and also subsumes a theorem of McCoy and Montgomery [18].…”

On the commutativity of certain rings

“…We shall give, in §3, an entirely elementary proof of this theorem for the special case in which R is of prime characteristic p and a p = a for every element a of R. Such a ring is a p-ring [4], which is perhaps the simplest and most natural generalization of a Boolean ring.…”

The representation of Boolean algebras

“…These two interpretations strongly suggest that the desired construction can in general be effected only by an appeal to inductive methods, based on mathematical (or complete) induction in the case of countably infinite Boolean rings and on transfinite induction in the higher cases. [25], and by McCoy and Montgomery [22]. It should be carefully observed, however, that certain of these constructions may be regarded as contained in somewhat earlier results established by Krull, Lindenbaum, Tarski, and Ulam.…”