Abstract:Let $A$ be a uniformly complete almost $f$-algebra and a natural number $p\in \{3,4,...\}$. Then $\Pi _{p}(A)= \{a_{1}...a_{p}; a_{k}\in A, k=1,...,p\}$ 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.
Keywords: vector lattice, uniformly complete vector lattice, lattice ordered algebra, almost $f$-algebra, $d$-algebra, $f$-algebra
AMS Subject Classification: 06F25, 46A40