Idempotents and the multiplicative group of some totally bounded rings

Mohamed A. Salim; Adela Tripe

doi:10.1007/s10587-011-0069-z

Idempotents and the multiplicative group of some totally bounded rings

Mohamed A. Salim, Adela Tripe

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

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 ^א0 commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.

Original language	English
Pages (from-to)	509-519
Number of pages	11
Journal	Czechoslovak Mathematical Journal
Volume	61
Issue number	2
DOIs	https://doi.org/10.1007/s10587-011-0069-z
Publication status	Published - Jun 2011

Keywords

Jacobson radical
Mersenne number
compact ring
group of units
left linearly compact ring
monothetic group
primary ring
summable set
totally bounded ring

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s10587-011-0069-z

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AU - Tripe, Adela

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AB - 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 א0 commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.

KW - Jacobson radical

KW - Mersenne number

KW - compact ring

KW - group of units

KW - left linearly compact ring

KW - monothetic group

KW - primary ring

KW - summable set

KW - totally bounded ring

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Idempotents and the multiplicative group of some totally bounded rings

Abstract

Keywords

ASJC Scopus subject areas

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