Abstract
In this paper, we show that the multiplicative derivations on J(α)-axial algebras, with α≠1,0,12, are additive under suitable conditions, which nowadays are called Martindale-type conditions. Besides, with proper assumptions, we proceed to study the additivity of multiplicative isomorphisms and derivations in the context of M(α,β)-axial algebras, except for multiplicative derivations when β=12. In this case, we mention a research question at the end.
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