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On some additive mappings on division rings | ||
| Journal of Algebra and Related Topics | ||
| دوره 9، شماره 2، اسفند 2021، صفحه 101-110 اصل مقاله (251.44 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2021.19142.1263 | ||
| نویسندگان | ||
| S. Ali* 1؛ A. Abdelwanis2 | ||
| 1Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, India | ||
| 2Department of Mathematics Faculty of Science Cairo University Giza 12613, Egypt | ||
| چکیده | ||
| Let $D$ be a division ring such that char$(D) \neq 2$ and $\alpha,\beta:D\rightarrow D$ be automorphisms of $D$. The main purpose of this paper is to characterizes additive maps $f$ and $g$ satisfying the identity $f(x)\alpha(x^{-1}) + \beta(x)g(x^{-1}) = 0$ for all $0 \neq x\in D.$ As an application, we describe the structure of an additive map $f$ satisfying the identity $f(x)\alpha(y)+\beta(x)f(y) =l$ for all $x,y\in D$ such that $xy=a,$ where $l,a\in D$ and $a$ is nonzero. With this, many known results can be either generalized or deduced. In particular, we generalized the results proved in \cite{C1} and \cite{C2}, respectively. | ||
| کلیدواژه‌ها | ||
| Division ring؛ derivation؛ $(alpha؛ beta)$-derivation؛ functional identity | ||
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