On generalized Jordan $\ast$-derivations with associated Hochschild $\ast$-2-cocycles

	On generalized Jordan $\ast$-derivations with associated Hochschild $\ast$-2-cocycles
International Journal of Nonlinear Analysis and Applications
مقاله 170، دوره 14، شماره 1، فروردین 2023، صفحه 2155-2167 اصل مقاله (388.64 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.26668.3382
نویسندگان
Javad Bakhti¹؛ Gholamreza Abbaspour Tabadkan^* ¹؛ Amin Hosseini²
¹School of Mathematics, University of Damghan, Damghan, Iran
²Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran
چکیده
In this paper, we introduce the notions of generalized $\ast$-derivations, generalized Jordan $\ast$-derivations and Jordan triple $\ast$-derivations with the associated Hochschild $\ast$-2-cocycles and then it is proved that if $\mathcal{R}$ is a prime $\ast$-ring and $f:\mathcal{R} \rightarrow \mathcal{R}$ is a nonzero generalized $\ast$-derivation with an associated Hochschild $\ast$-2-cocycle $\beta$, then $\mathcal{R}$ is commutative. Some other results regarding generalized Jordan $\ast$-derivations are also established.
کلیدواژه‌ها
$\ast$-derivation؛ generalized Jordan $\ast$-derivation؛ Hochschild $\ast$-2-cocycle؛ $\ast$-ring؛ prime (semiprime) ring
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