| Title:
|
An elementary proof of a theorem on sublattices of finite codimension (English) |
| Author:
|
Wójtowicz, Marek |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
99-100 |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper presents an elementary proof and a generalization of a theorem due to Abramovich and Lipecki, concerning the nonexistence of closed linear sublattices of finite codimension in nonatomic locally solid linear lattices with the Lebesgue property. (English) |
| Keyword:
|
linear lattice |
| Keyword:
|
Lebesgue property |
| Keyword:
|
lattice homomorphism |
| MSC:
|
46A40 |
| MSC:
|
47B65 |
| idZBL:
|
Zbl 0937.46002 |
| idMR:
|
MR1622986 |
| . |
| Date available:
|
2009-01-08T18:39:19Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118989 |
| . |
| Reference:
|
[1] Abramovich Y.A., Lipecki Z.: On ideals and sublattices in linear lattices and $F$-lattices.Math. Proc. Cambridge Phil. Soc. 108 (1990), 79-87. Zbl 0751.46009, MR 1049761 |
| Reference:
|
[2] Aliprantis C.D., Burkinshaw O.: Locally Solid Riesz Spaces.Academic Press, 1978. Zbl 1043.46003, MR 0493242 |
| Reference:
|
[3] Luxemburg W.A.J., Zaanen A.C.: Riesz Spaces I.North-Holland, 1971. |
| . |
