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.
@article{119206,
author = {Karim Boulabiar},
title = {Products in almost $f$-algebras},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {41},
year = {2000},
pages = {747-759},
zbl = {1048.06011},
mrnumber = {1800169},
language = {en},
url = {http://dml.mathdoc.fr/item/119206}
}
Boulabiar, Karim. Products in almost $f$-algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 747-759. http://gdmltest.u-ga.fr/item/119206/
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