| Title:
|
Ojective ideals in modular lattices (English) |
| Author:
|
Nimbhorkar, Shriram K. |
| Author:
|
Shroff, Rupal C. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
161-178 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The concept of an extending ideal in a modular lattice is introduced. A translation of module-theoretical concept of ojectivity (i.e. generalized relative injectivity) in the context of the lattice of ideals of a modular lattice is introduced. In a modular lattice satisfying a certain condition, a characterization is given for direct summands of an extending ideal to be mutually ojective. We define exchangeable decomposition and internal exchange property of an ideal in a modular lattice. It is shown that a finite decomposition of an extending ideal is exchangeable if and only if its summands are mutually ojective. (English) |
| Keyword:
|
modular lattice |
| Keyword:
|
essential ideal |
| Keyword:
|
max-semicomplement |
| Keyword:
|
extending ideal |
| Keyword:
|
direct summand |
| Keyword:
|
exchangeable decomposition |
| Keyword:
|
ojective ideal |
| MSC:
|
06B10 |
| MSC:
|
06C05 |
| MSC:
|
16D10 |
| idZBL:
|
Zbl 06433727 |
| idMR:
|
MR3336031 |
| DOI:
|
10.1007/s10587-015-0166-5 |
| . |
| Date available:
|
2015-04-01T12:30:16Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144219 |
| . |
| 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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| . |
