Abstract:
Let $E$ be a unital $f$-module over an $f$-algebra $A$. With the help of Arens extension theory, a $(A^{\sim})_{n}^{\sim}$ module
structure on $E^{\sim}$ can be defined. The paper deals mainly with properties of
the Arens homomorphism
$\eta\colon(A^{\sim})_{n}^{\sim}\to \operatorname{Orth}(E^{\sim})$, which is defined by
the $(A^{\sim})_{n}^{\sim}$ module
structure on $E^{\sim}$. Necessary and sufficient conditions
for an $A$ submodule of
$E$ to be an order ideal are obtained.
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