The image of Jordan left derivations on algebras

Amin Hosseini; Ajda Fosner

doi:10.5269/bspm.v38i6.40084

Amin Hosseini Kashmar Higher Educations Institute Department of Mathematics
Ajda Fosner University of Primorska Faculty of Management

DOI: https://doi.org/10.5269/bspm.v38i6.40084

Keywords: left derivation, Jordan left derivation, complex algebra, Jacobson radical.

Abstract

Let A be an algebra, and let I be a semiprime ideal of A. Suppose that

d : A → A is a Jordan left derivation such that d(I) ⊆ I.

We prove that if dim{d(a)+I : a ⋲ A} ≤ 1, then d(A) ⊆ I. Additionally, we consider several consequences of this result.

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