Abstract
In this paper, we introduce the notion of b -algebras and we give some related properties. To be more precise, we call a b -algebra any lattice-ordered algebra A the bands of which are closed under multiplication. We obtain that A can be identified with the reals whenever A is an Archimedean b -algebra with unit element e > 0 and such that every positive element has an inverse. This improves a result by Huijsmans who got the same conclusion for f -algebras imposing the extra condition of positivity of inverses. Moreover, we show that the order continuous bidual ( A ∼ ) n ∼ of an Archimedean b -algebra A is a b -algebra with respect to the Arens multiplication. Furthermore, if the b -algebra A has positive squares, then the order bidual A ∼ ∼ is again a b -algebra.
Published Version
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