## Almost $$f$$-algebras: Structure and the Dedekind completion.(English)Zbl 0967.46008

The authors discuss the structure of almost $$f$$-algebra and prove that the multiplication on an Archimedean almost $$f$$-algebra $$E$$ extends to an almost $$f$$-algebra multiplication on the Dedekind completion of $$E$$, thus answering a question by the late C. B. Huijsmans.

### MSC:

 46A40 Ordered topological linear spaces, vector lattices 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces

### Keywords:

$$f$$-algebra; structure; Dedekind completion
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