# Article

Full entry | PDF   (0.2 MB)
Keywords:
vector lattice; uniformly complete vector lattice; lattice ordered algebra; almost $f$-algebra; $d$-algebra; $f$-algebra
Summary:
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.
References:
[1] Basly M., Triki A.: $FF$-algébres Archimédiennes réticulées. University of Tunis, preprint, 1988. MR 0964828
[2] Bernau S.J, Huijsmans C.B.: Almost $f$-algebras and $d$-algebras. Math. Proc. Camb. Phil. Soc. 107 (1990), 287-308. MR 1027782 | Zbl 0707.06009
[3] Beukers F., Huijsmans C.B.: Calculus in $f$-algebras. J. Austral. Math. Soc. (Series A) 37 (1984), 110-116. MR 0742249 | Zbl 0555.06014
[4] Boulabiar K.: A relationship between two almost $f$-algebra products. Algebra Univ., to appear. MR 1785321 | Zbl 1012.06022
[5] Buskes G., van Rooij A.: Almost $f$-algebras: structure and the Dedekind completion. in Three papers on Riesz spaces and almost $f$-algebras, Technical Report, Catholic University Nijmegen, Report 9526, 1995. Zbl 0967.46008
[6] Huijsmans C.B., de Pagter B.: Averaging operators and positive contractive projections. J. Math. Appl. 113 (1986), 163-184. MR 0826666 | Zbl 0604.47024
[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. MR 0704021 | Zbl 0519.46001

Partner of