Weak right η-centralizers of prime rings

Abstract

This work encompasses the study of certain weak maps termed as weak right η-centralizers defined on $\mathfrak{D}$ a noncommutative prime ring to ${\mathfrak{Q}}_{\mathrm{ml}}(\mathfrak{D})$. The first section provides an overview of the motivation behind our work. In the second section, our main focus is to establish the characterization of weak right η-centralizers while addressing the theory of functional identities, particularly in the challenging case of low dimensions. Furthermore, in the third section, we derive the characterization of weak Jordan σ-derivations based on the aforementioned characterization.

Keywords:

• Prime ring
• derivation
• maximal left ring of quotients
• polynomial identity (PI)
• generalized polynomial identity (GPI)
• functional identity (FI)

2020 AMS Subject Classifications:

• 16R60
• 16N60
• 16W25
• 16W20

Disclosure statement

No potential conflict of interest was reported by the author(s).

Funding

This research received no specific grant from any funding agency.

Authors contributions

The authors declare that all the research and writing has been done together.

Ethical approval

Not applicable to this article.

Availability of data and materials

Not applicable to this article as no datasets were generated or analysed during the current study.