Reverse ∗-Jordan type maps on Jordan ∗-algebras

Abstract

Let [Formula: see text] and [Formula: see text] be two ∗-Jordan algebras with identities [Formula: see text] and [Formula: see text], respectively, and [Formula: see text] a nontrivial ∗-idempotent in [Formula: see text]. In this paper, we study the characterization of multiplicative ∗-Jordan-type maps. In particular, we provide a characterization in the case of unital prime associative algebra endowed with an involution.

On ∗-reverse derivable maps

“…For the case of non-associative rings and algebras having nontrivial idempotents, additivity of various maps defined on them has already been proved in the literature. In alternative rings, we can mention the works in [6,7,8,9,10,11,12,13].…”

Nonlinear *-Jordan-type derivations on alternative *-algebras

“…The study on characterizations of certain maps on non-associative algebraic structures has become an active and broad line of research in recent years, we can mention [2,5,6,7,8,9,10,11]. For the case of associative structures Brešar and Fošner in [1,12], presented the following definition: for a, b ∈ R, where R is a * -ring, we denote by {a, b} * = ab + ba * and [a, b] * = ab − ba * the * -Jordan product and the * -Lie product, respectively.…”