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Keywords:
compact ring; group of units; Jacobson radical; left linearly compact ring; Mersenne number; monothetic group; primary ring; summable set; totally bounded ring
compact ring; group of units; Jacobson radical; left linearly compact ring; Mersenne number; monothetic group; primary ring; summable set; totally bounded ring
Summary:
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 $2^{\aleph _0}$ commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.
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