| Title:
|
Idempotents and the multiplicative group of some totally bounded rings (English) |
| Author:
|
Salim, Mohamed A. |
| Author:
|
Tripe, Adela |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
509-519 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
compact ring |
| Keyword:
|
group of units |
| Keyword:
|
Jacobson radical |
| Keyword:
|
left linearly compact ring |
| Keyword:
|
Mersenne number |
| Keyword:
|
monothetic group |
| Keyword:
|
primary ring |
| Keyword:
|
summable set |
| Keyword:
|
totally bounded ring |
| MSC:
|
16U60 |
| MSC:
|
16W80 |
| MSC:
|
22C05 |
| MSC:
|
22D05 |
| idZBL:
|
Zbl 1240.16049 |
| idMR:
|
MR2905419 |
| DOI:
|
10.1007/s10587-011-0069-z |
| . |
| Date available:
|
2011-06-06T10:38:17Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141549 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
