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vector lattice; uniformly complete vector lattice; lattice ordered algebra; almost $f$-algebra; $d$-algebra; $f$-algebra
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.
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