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
- General Mathematics