- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 On generalized Jordan derivations of generalized matrix algebras Commun. Korean Math. Soc. 2020 Vol. 35, No. 3, 733-744 https://doi.org/10.4134/CKMS.c190362Published online July 5, 2020 Mohammad Ashraf, Aisha Jabeen Aligarh Muslim University; Jamia Millia Islamia Abstract : Let $\mathfrak{R}$ be a commutative ring with unity, $\mathrm{A}$ and $\mathrm{B}$ be $\mathfrak{R}$-algebras, $\mathrm{M}$ be a $(\mathrm{A}, \mathrm{B})$-bimodule and $\mathrm{N}$ be a $(\mathrm{B}, \mathrm{A})$-bimodule. The $\mathfrak{R}$-algebra $\mathfrak{S}=\mathfrak{S}(\mathrm{A}, \mathrm{M}, \mathrm{N}, \mathrm{B})$ is a generalized matrix algebra defined by the Morita context $(\mathrm{A}, \mathrm{B}, \mathrm{M}, \mathrm{N}, \xi_{\mathrm{M}\mathrm{N}}, \Omega_{\mathrm{N}\mathrm{M}})$. In this article, we study generalized derivation and generalized Jordan derivation on generalized matrix algebras and prove that every generalized Jordan derivation can be written as the sum of a generalized derivation and antiderivation with some limitations. Also, we show that every generalized Jordan derivation is a generalized derivation on trivial generalized matrix algebra over a field. Keywords : Generalized matrix algebras, generalized derivation, Jordan derivation MSC numbers : 47L35, 15A78, 16W25 Supported by : This research is supported by Dr. D. S. Kothari Postdoc-toral Fellowship under University Grants Commission (Grant No. F.4-2/2006(BSR)/MA/18-19/0014), awarded to the second author. Downloads: Full-text PDF   Full-text HTML