| Title:
|
A class of multiplicative lattices (English) |
| Author:
|
Dumitrescu, Tiberiu |
| Author:
|
Epure, Mihai |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
591-601 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the multiplicative lattices $L$ which satisfy the condition $ a=(a :\nobreak (a: \nobreak b))(a:b) $ for all $a,b\in L$. Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group $\mathbb {Z}$ or $\mathbb {R}$. A sharp lattice $L$ localized at its maximal elements are totally ordered sharp lattices. The converse is true if $L$ has finite character. (English) |
| Keyword:
|
multiplicative lattice |
| Keyword:
|
Prüfer lattice |
| Keyword:
|
Prüfer integral domain |
| MSC:
|
06F99 |
| MSC:
|
13A15 |
| MSC:
|
13F05 |
| idZBL:
|
07361087 |
| idMR:
|
MR4263188 |
| DOI:
|
10.21136/CMJ.2021.0034-20 |
| . |
| Date available:
|
2021-05-20T13:48:43Z |
| Last updated:
|
2023-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148923 |
| . |
| 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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| . |
