| Title:
|
Order complex of ideals in a commutative ring with identity (English) |
| Author:
|
Milošević, Nela |
| Author:
|
Petrović, Zoran Z. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
947-952 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Order complex is an important object associated to a partially ordered set. Following a suggestion from V. A. Vassiliev (1994), we investigate an order complex associated to the partially ordered set of nontrivial ideals in a commutative ring with identity. We determine the homotopy type of the geometric realization for the order complex associated to a general commutative ring with identity. We show that this complex is contractible except for semilocal rings with trivial Jacobson radical when it is homotopy equivalent to a sphere. (English) |
| Keyword:
|
ideal |
| Keyword:
|
commutative ring |
| Keyword:
|
order complex |
| Keyword:
|
homotopy type |
| MSC:
|
05E40 |
| MSC:
|
06A07 |
| MSC:
|
13A99 |
| MSC:
|
55P15 |
| idZBL:
|
Zbl 06537702 |
| idMR:
|
MR3441327 |
| DOI:
|
10.1007/s10587-015-0219-9 |
| . |
| Date available:
|
2016-01-13T09:06:37Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144784 |
| . |
| Reference:
|
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