Article

An identity in prime superalgebras

Published in: Quaestiones Mathematicae
Volume 42 , issue 4 , 2019 , pages: 451–464

DOI: 10.2989/16073606.2018.1458756

Author(s): Ajda Fošner Faculty of management, Slovenia , Maja Fošner Faculty of logistics, Slovenia , Benjamin Marcen Faculty of logistics, Slovenia

Keywords: 17A70 , 17B01 , 17B40 , 17A70 , 17B01 , 17B40

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Abstract

In this paper we investigate the functional identity in a prime associative superalgebras. We prove the following result. Suppose that there exists a nonzero additive mapping f = f₀ + f₁, on a prime associative superalgebra with char(R) ≠ 2, satisfying the relation [f (x), y²] = 0 for all x, y ∈ ℋ(). If

is prime algebra then [f (), ] = 0 or [, ] = 0.

₀ is prime algebra then [f (), ] = 0 and [, ₀] = 0 or A is trivial. More- over, if C₁ = 0 then f₀(₁) = 0 and f₁(₀) = 0.