Arens regularity of lattice-ordered rings
This work discusses the problem of Arens regularity of a lattice-ordered ring. In this prospect, a counterexample is furnished to show that without extra conditions, a lattice-ordered ring need not be Arens regular. However, as shown in this paper, it turns out that any -ring in the sense of Birkhoff and Pierce is Arens regular. This result is then used and extended to the more general setting of almost -rings introduced again by Birkhoff.