Archimedean l-algebras with multiplication closed bands

作者：Turan Bahri^*; Aslantas Mustafa

来源：Indagationes Mathematicae, 2014, 25(3): 588-595.

DOI：10.1016/j.indag.2014.02.003

• f-algebra
• b-algebra
• Arens multiplication
• Bidual
• Order continuous bidual

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(similar to))(n) over tilde 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(similar to similar to) is again a b-algebra.

• 出版日期2014-4-18