| Title:
|
Products in almost $f$-algebras (English) |
| Author:
|
Boulabiar, K. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
747-759 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $A$ be a uniformly complete almost $f$-algebra and a natural number $p\in\{3,4,\dots \}$. Then $\Pi_{p}(A)= \{a_{1}\dots a_{p}; a_{k}\in A, k=1,\dots ,p\}$ is a uniformly complete semiprime $f$-algebra under the ordering and multiplication inherited from $A$ with $\Sigma_{p}(A)=\{a^{p}; 0\leq a\in A\}$ as positive cone. (English) |
| Keyword:
|
vector lattice |
| Keyword:
|
uniformly complete vector lattice |
| Keyword:
|
lattice ordered algebra |
| Keyword:
|
almost $f$-algebra |
| Keyword:
|
$d$-algebra |
| Keyword:
|
$f$-algebra |
| MSC:
|
06F25 |
| MSC:
|
46A40 |
| idZBL:
|
Zbl 1048.06011 |
| idMR:
|
MR1800169 |
| . |
| Date available:
|
2009-01-08T19:06:56Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119206 |
| . |
| Reference:
|
[1] Basly M., Triki A.: $FF$-algébres Archimédiennes réticulées.University of Tunis, preprint, 1988. MR 0964828 |
| Reference:
|
[2] Bernau S.J, Huijsmans C.B.: Almost $f$-algebras and $d$-algebras.Math. Proc. Camb. Phil. Soc. 107 (1990), 287-308. Zbl 0707.06009, MR 1027782 |
| Reference:
|
[3] Beukers F., Huijsmans C.B.: Calculus in $f$-algebras.J. Austral. Math. Soc. (Series A) 37 (1984), 110-116. Zbl 0555.06014, MR 0742249 |
| Reference:
|
[4] Boulabiar K.: A relationship between two almost $f$-algebra products.Algebra Univ., to appear. Zbl 1012.06022, MR 1785321 |
| Reference:
|
[5] Buskes G., van Rooij A.: Almost $f$-algebras: structure and the Dedekind completion.in Three papers on Riesz spaces and almost $f$-algebras, Technical Report, Catholic University Nijmegen, Report 9526, 1995. Zbl 0967.46008 |
| Reference:
|
[6] Huijsmans C.B., de Pagter B.: Averaging operators and positive contractive projections.J. Math. Appl. 113 (1986), 163-184. Zbl 0604.47024, MR 0826666 |
| Reference:
|
[7] Luxembourg W.A.J., Zaanen A.C.: Riesz spaces I.North-Holland, Amsterdam, 1971. |
| Reference:
|
[8] de Pagter B.: $f$-algebras and orthomorphisms.Thesis, Leiden, 1981. |
| Reference:
|
[9] Zaanen A.C.: Riesz spaces II.North-Holland, Amsterdam, 1983. Zbl 0519.46001, MR 0704021 |
| . |
