Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2024; 39(1): 79-91

Online first article January 25, 2024      Printed January 31, 2024

https://doi.org/10.4134/CKMS.c230128

Copyright © The Korean Mathematical Society.

Results of 3-derivations and commutativity for prime rings with involution involving symmetric and skew symmetric components

Hanane AHARSSI, Kamal CHARRABI, Abdellah MAMOUNI

Moulay Isma\"{i}l University; Moulay Isma\"{i}l University; Moulay Isma\"{i}l University

Abstract

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This article examines the connection between 3-derivations and the commutativity of a prime ring $R$ with an involution $\ast$ that fulfills particular algebraic identities for symmetric and skew symmetric elements. In practice, certain well-known problems, such as the Herstein problem, have been studied in the setting of three derivations in involuted rings.

Keywords: Prime ring, involution, commutativity, generalized derivation, symmetric elements, skew symmetric elements

MSC numbers: 16N60, 16W10, 16W25

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