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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 | ||
آمار تعداد مشاهده مقاله: 677 تعداد دریافت فایل اصل مقاله: 908 |