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In this paper, we prove that under certain conditions the enveloping-algebra of an AJW-algebra is an AW-algebra. Applying this, we prove that an extension of a derivation of a reversible JC-algebra  A  to a-derivation of the C-algebra generated by  A  is unique, and reversible AJW-algebras, satisfying certain conditions, have only inner derivations.

Enveloping -algebras and derivations of Baer JB-algebras