Archimedean l-algebras with multiplication closed bands

TURAN B., Aslantas M.

INDAGATIONES MATHEMATICAE-NEW SERIES, cilt.25, sa.3, ss.588-595, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 3
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.indag.2014.02.003
  • Dergi Adı: INDAGATIONES MATHEMATICAE-NEW SERIES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.588-595
  • Gazi Üniversitesi Adresli: Evet

Özet

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. (C) 2014 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.