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When the image of a derivation on a uniformly complete 𝑓-algebra is contained in the radical
Forum Mathematicum ( IF 1.0 ) Pub Date : 2020-08-06 , DOI: 10.1515/forum-2016-0082
Mohamed Ali Toumi 1
Affiliation  

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.

中文翻译:

当一个一致完备的𝑓-代数上的导数的形象包含在部首中时

摘要 1977 年,Colville、Davis 和 Keimel [F 形环的正推导,J. Aust。数学。社会。爵士。A 23 1977, 3, 371–375] 证明了对阿基米德 f-代数 A 的正推导在 A 的幂零元集合中具有其范围。 本文的主要目的是获得上述 Colville 的推广, Davis 和 Keimel 得出一般推导。此外,我们给出了一个新版本的 Singer-Wermer 猜想,用于作用于一致完备的几乎 f 代数的二阶导数类。
更新日期:2020-08-06
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