Research Article

Derivations in disjointly complete commutative regular algebras

Published in: Quaestiones Mathematicae
Volume 47 , issue sup1 , 2024 , pages: 23–86

DOI: 10.2989/16073606.2023.2287814

Author(s): Aleksey Ber National University of Uzbekistan, Uzbekistan , Vladimir Chilin North-Ossetian State University, Russia , Fedor Sukochev UNSW, Australia

Keywords: 47B47 , 13N15 , 46J05 , Derivations , disjointly complete regular algebras , Wickstead problem

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Abstract

We show that any nonexpansive derivation on a subalgebra of a dis-jointly complete commutative regular algebra extends up to a derivation on . For an algebra of functions , continuous on a dense open subset of Stone compact X, we establish that the lack of nontrivial derivation is equivalent to σ-distributivity of the Boolean algebra of clopen subsets of X. The field is an arbitrary normed field of charachteristic zero containing a complete non-discrete subfield. Our work is motivated by two seemingly unrelated problems due to Ayupov [2] and Wickstead [32].

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