New Concepts on Module Arens Regularity for Module Banach Algebras.

The main purpose of this paper is to introduce a new definition of JA‐module Arens regularity, which extends former standard definition. Then a new module structure on the semigroup algebra l1S as l1ES‐module with nontrivial right and left module actions is constructed. Using this construction, it is also proved that l1S is a Jl1S‐module Arens regular if and only if S/≈ is finite. [ABSTRACT FROM AUTHOR]