Geodesic
Idempotents and the multiplicative group of some totally bounded rings
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 509-519
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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 $2^{\aleph _0}$ commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.
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.
DOI : 10.1007/s10587-011-0069-z
Classification : 16U60, 16W80, 22C05, 22D05
Keywords: compact ring; group of units; Jacobson radical; left linearly compact ring; Mersenne number; monothetic group; primary ring; summable set; totally bounded ring 
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Salim, Mohamed A.; Tripe, Adela. Idempotents and the multiplicative group of some totally bounded rings. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 509-519. doi: 10.1007/s10587-011-0069-z

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