| Title:
|
Archimedean frames, revisited (English) |
| Author:
|
Martínez, Jorge |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
25-44 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper extends the notion of an archimedean frame to frames which are not necessarily algebraic. The new notion is called {\it joinfitness\/} and is {\it Choice-free\/}. Assuming the Axiom of Choice and for compact normal algebraic frames, the new and the old coincide. There is a subfunctor from the category of compact normal frames with skeletal maps with joinfit values, which is almost a coreflection. Conditions making it so are briefly discussed. The concept of an {\it infinitesimal\/} element arises naturally, and the join of suitably chosen infinitesimals defines the joinfit nucleus. The paper concludes with mostly Choice-free applications of these ideas to commutative rings and their radical ideals. (English) |
| Keyword:
|
archimedean lattice |
| Keyword:
|
joinfit coreflection |
| Keyword:
|
infinitesimals |
| Keyword:
|
fitness conditions |
| MSC:
|
06D22 |
| MSC:
|
18A32 |
| MSC:
|
18A40 |
| idZBL:
|
Zbl 1212.06025 |
| idMR:
|
MR2432818 |
| . |
| Date available:
|
2009-05-05T17:06:16Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119699 |
| . |
| Reference:
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| . |
