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 | |
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)