| Title:
|
Countable chains of distributive lattices as maximal semilattice quotients of positive cones of dimension groups (English) |
| Author:
|
Růžička, Pavel |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
11-20 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct a countable chain of Boolean semilattices, with all inclusion maps preserving the join and the bounds, whose union cannot be represented as the maximal semilattice quotient of the positive cone of any dimension group. We also construct a similar example with a countable chain of strongly distributive bounded semilattices. This solves a problem of F. Wehrung. (English) |
| Keyword:
|
semilattice |
| Keyword:
|
lattice |
| Keyword:
|
distributive |
| Keyword:
|
dimension group |
| Keyword:
|
direct limit |
| MSC:
|
06A12 |
| MSC:
|
06B15 |
| MSC:
|
06D05 |
| MSC:
|
06F20 |
| MSC:
|
20K25 |
| idZBL:
|
Zbl 1138.06003 |
| idMR:
|
MR2223963 |
| . |
| Date available:
|
2009-05-05T16:55:12Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119570 |
| . |
| 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:
|
[7] Grätzer G.: General Lattice Theory.second edition, Birkhäuser, Basel, 1998, xix + 663 pp. MR 1670580 |
| Reference:
|
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| Reference:
|
[9] Schmidt E.T.: Zur Charakterisierung der Kongruenzverbände der Verbände.Mat. Časopis Sloven. Akad. Vied 18 (1968), 3-20. MR 0241335 |
| Reference:
|
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| Reference:
|
[11] Wehrung F.: Representation of algebraic distributive lattices with $\aleph_1$ compact elements as ideal lattices of regular rings.Publ. Mat. (Barcelona) 44 (2000), 419-435. Zbl 0989.16010, MR 1800815 |
| Reference:
|
[12] Wehrung F.: Semilattices of finitely generated ideals of exchange rings with finite stable rank.Trans. Amer. Math. Soc. 356 5 (2004), 1957-1970. Zbl 1034.06007, MR 2031048 |
| Reference:
|
[13] Wehrung F.: Forcing extensions of partial lattices.J. Algebra 262 1 (2003), 127-193. Zbl 1030.03039, MR 1970805 |
| . |
