Multiplicative bi-skew Jordan triple derivations on prime β-algebra
Abdul Nadim Khan, Husain Alhazmi
Abstract
Abstract Let π be a prime β-algebra. For any <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mi mathvariant="script">A</m:mi> <m:mo>,</m:mo> <m:mi mathvariant="script">B</m:mi> </m:mrow> <m:mo>β</m:mo> <m:mi mathvariant="script">A</m:mi> </m:mrow> </m:math> \mathscr{A},\mathscr{B}\in\mathcal{A} , a product <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mi mathvariant="script">A</m:mi> <m:mo lspace="0.222em" rspace="0.222em">β</m:mo> <m:mi mathvariant="script">B</m:mi> </m:mrow> <m:mo>=</m:mo> <m:mrow> <m:mrow> <m:mi mathvariant="script">A</m:mi> <m:mo>β’</m:mo> <m:msup> <m:mi mathvariant="script">B</m:mi> <m:mo>*</m:mo> </m:msup> </m:mrow> <m:mo>+</m:mo> <m:mrow> <m:mi mathvariant="script">B</m:mi> <m:mo>β’</m:mo> <m:msup> <m:mi mathvariant="script">A</m:mi> <m:mo>*</m:mo> </m:msup> </m:mrow> </m:mrow> </m:mrow> </m:math> \mathscr{A}\star\mathscr{B}=\mathscr{A}\mathscr{B}^{*}+\mathscr{B}\mathscr{A}^{*} is called a bi-skew Jordan product. In this paper, it is shown that every multiplicative bi-skew Jordan triple derivation is an additive β-derivation on a prime β-algebra.