Abstract
In this paper, using derivation theory, we present some results concerning the automatic order boundedness of band preserving operators on Archimedean semiprime \(f\)-algebras. Finally, inspired by the proof of Bernau and Huijsmans (Math Proc Camb Philos Soc 107:287–308, 1990), we give necessary and sufficient conditions for Archimedean lattice-ordered algebras to be commutative.
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