Supercentralizing Maps on Generalized Quaternion Rings

Document Type : Original Article

Authors

Ajda Fošner ¹

Leila Heidari Zadeh ²

¹ Faculty of Management, University of Primorska, Slovenia

² Department of Mathematics and Statistics, Shoushtar Branch, Islamic Azad University, Shoushtar, Iran

10.22034/kjm.2025.501627.3442

Abstract

Let $\mathcal A=H_{\alpha,\beta}(\mathcal{S})$ be a generalized quaternion ring over an arbitrary unital ring $\mathcal{S}$ with supercenter $\mathbb{Z}_s(\mathcal A)$. In this article, we provide the structure of supercentralizing additive map $F$ on a generalized quaternion superring $\mathcal A$ and demonstrate that $F$ on $\mathcal A$ is proper. Furthermore, we establish that any supercentralizing derivation on the quaternion ring is zero.

Keywords

Supercentralizing

generalized quaternions rings

$\mathbb{Z}_{2}$-graded rings

Subjects

• 47 Operator theory

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