Products in almost f -algebras

Karim Boulabiar

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 4, page 747-759
  • ISSN: 0010-2628

Abstract

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Let A be a uniformly complete almost f -algebra and a natural number p ∈ { 3 , 4 , ⋯ } . Then Π p ( A ) = { a 1 ⋯ a p ; a k ∈ A , k = 1 , ⋯ , p } is a uniformly complete semiprime f -algebra under the ordering and multiplication inherited from A with Σ p ( A ) = { a p ; 0 ≤ a ∈ A } as positive cone.

How to cite

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Boulabiar, Karim. "Products in almost $f$-algebras." Commentationes Mathematicae Universitatis Carolinae 41.4 (2000): 747-759. <http://eudml.org/doc/248636>.

@article{Boulabiar2000,
abstract = {Let $A$ be a uniformly complete almost $f$-algebra and a natural number $p\in \lbrace 3,4,\dots \rbrace $. Then $\Pi _\{p\}(A)= \lbrace a_\{1\}\dots a_\{p\}; a_\{k\}\in A, k=1,\dots ,p\rbrace $ is a uniformly complete semiprime $f$-algebra under the ordering and multiplication inherited from $A$ with $\Sigma _\{p\}(A)=\lbrace a^\{p\}; 0\le a\in A\rbrace $ as positive cone.},
author = {Boulabiar, Karim},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {vector lattice; uniformly complete vector lattice; lattice ordered algebra; almost $f$-algebra; $d$-algebra; $f$-algebra; uniformly complete vector lattice; lattice-ordered algebra; almost -algebra; -algebra},
language = {eng},
number = {4},
pages = {747-759},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Products in almost $f$-algebras},
url = {http://eudml.org/doc/248636},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Boulabiar, Karim
TI - Products in almost $f$-algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 4
SP - 747
EP - 759
AB - Let $A$ be a uniformly complete almost $f$-algebra and a natural number $p\in \lbrace 3,4,\dots \rbrace $. Then $\Pi _{p}(A)= \lbrace a_{1}\dots a_{p}; a_{k}\in A, k=1,\dots ,p\rbrace $ is a uniformly complete semiprime $f$-algebra under the ordering and multiplication inherited from $A$ with $\Sigma _{p}(A)=\lbrace a^{p}; 0\le a\in A\rbrace $ as positive cone.
LA - eng
KW - vector lattice; uniformly complete vector lattice; lattice ordered algebra; almost $f$-algebra; $d$-algebra; $f$-algebra; uniformly complete vector lattice; lattice-ordered algebra; almost -algebra; -algebra
UR - http://eudml.org/doc/248636
ER -

References

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  1. Basly M., Triki A., F F -algébres Archimédiennes réticulées, University of Tunis, preprint, 1988. MR0964828
  2. Bernau S.J, Huijsmans C.B., Almost f -algebras and d -algebras, Math. Proc. Camb. Phil. Soc. 107 (1990), 287-308. (1990) Zbl0707.06009MR1027782
  3. Beukers F., Huijsmans C.B., Calculus in f -algebras, J. Austral. Math. Soc. (Series A) 37 (1984), 110-116. (1984) Zbl0555.06014MR0742249
  4. Boulabiar K., A relationship between two almost f -algebra products, Algebra Univ., to appear. Zbl1012.06022MR1785321
  5. Buskes G., van Rooij A., Almost f -algebras: structure and the Dedekind completion, in Three papers on Riesz spaces and almost -algebras, Technical Report, Catholic University Nijmegen, Report 9526, 1995. Zbl0967.46008
  6. Huijsmans C.B., de Pagter B., Averaging operators and positive contractive projections, J. Math. Appl. 113 (1986), 163-184. (1986) Zbl0604.47024MR0826666
  7. Luxembourg W.A.J., Zaanen A.C., Riesz spaces I, North-Holland, Amsterdam, 1971. 
  8. de Pagter B., f -algebras and orthomorphisms, Thesis, Leiden, 1981. 
  9. Zaanen A.C., Riesz spaces II, North-Holland, Amsterdam, 1983. Zbl0519.46001MR0704021

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