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f-algebras in which order ideals are ring ideals. (English) Zbl 0662.46006

The paper deals with f-algebras, i.e. vector lattices A with an associative multiplication preserving the positive cone \(A^+\) and such that \((xy)\wedge z=z\wedge (xy)=0\) for all disjoint x, z and all \(y\in A^+\). The main result gives conditions under which every order ideal in A is a ring ideal (i.e. an algebra ideal).
Reviewer: B.Riecan

MSC:

46A40 Ordered topological linear spaces, vector lattices
06F25 Ordered rings, algebras, modules
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