Order completions of semiprime rings

Walter D. Burgess; Robert M. Raphael

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In this paper, we extend some results of D. Dolzan on finite rings to profinite rings, a complete classification of profinite commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family of power $2^{ℵ_{0}}$ commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.