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On algebra homomorphisms in complex almost $$f$$-algebras. (English) Zbl 1070.06008
Summary: Extensions of order-bounded linear operators on an Archimedean vector lattice to its relatively uniform completion are considered and are applied to show that the multiplication in an Archimedean lattice-ordered algebra can be extended, in a unique way, to its relatively uniform completion. This is applied to show, among other things, that any order-bounded algebra homomorphism on a complex Archimedean almost $$f$$-algebra is a lattice homomorphism.

##### MSC:
 06F25 Ordered rings, algebras, modules 46A40 Ordered topological linear spaces, vector lattices 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
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