Geodesic
On the Arens Homomorphism
Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 2, pp. 82-91.

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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.
Keywords: Riesz space, orthomorphism
Mots-clés : $f$-module, Arens homomorphism. 
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B. Turan; M. Aslantaş. On the Arens Homomorphism. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 2, pp. 82-91. http://geodesic.mathdoc.fr/item/FAA_2022_56_2_a7/

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