Theorem.2.3 Let R be a finite Boolean ring
.Then [absolute value of ([R.sup.x])] = 1.
It follows that the proper subset A, a maximal set of B forms a Boolean ring. B is a Boolean-near-ring, whose proper subset is a Boolean-ring, then by definition, B is a SmarandacheBoolean-near-ring.
Hence A is a maximal set with uni-element and by theorem 1 and definition A, a maximal set of B forms a Boolean ring.
Ryabukhin, "Boolean ring
," in Encyclopaedia of Mathematics, M.
In the literature such rings exist naturally, for instance, the rings [Z.sub.6] (modulo integers), [Z.sub.10] (modulo integers), Boolean ring