# Products in almost $f$-algebras

Commentationes Mathematicae Universitatis Carolinae (2000)

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

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topBoulabiar, 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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- Zaanen A.C., Riesz spaces II, North-Holland, Amsterdam, 1983. Zbl0519.46001MR0704021

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