When the image of a derivation on a uniformly complete 𝑓-algebra is contained in the radical

Mohamed Ali Toumi 1
  • 1 Laboratoire d’Ingénierie Mathématique, Ecole Polytechnique de Tunisie, and Département de Mathématiques, Faculté des Sciences de Bizerte, Université de Carthage, 7021 Zarzouna, Bizerte, Tunisia
Mohamed Ali Toumi
  • Corresponding author
  • Laboratoire d’Ingénierie Mathématique, Ecole Polytechnique de Tunisie, and Département de Mathématiques, Faculté des Sciences de Bizerte, Université de Carthage, 7021 Zarzouna, Bizerte, Tunisia
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Abstract

In 1977, Colville, Davis, and Keimel [Positive derivations on f-rings, J. Aust. Math. Soc. Ser. A 23 1977, 3, 371–375] proved that a positive derivation on an Archimedean f-algebra A has its range in the set of nilpotent elements of A. The main objective of this paper is to obtain a generalization of the above Colville, Davis and Keimel result to general derivations. Moreover, we give a new version of the Singer–Wermer conjecture for the class of second-order derivations acting on uniformly complete almost f-algebras.

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