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RESEARCH ARTICLE
Some commutativity criteria for $3$-prime near rings
A. Raji LMACS Laboratory, Faculty of Sciences and Technology, Sultan Moulay Slimane University, P.O.Box 523, 23000, Beni Mellal, Morocco
Abstract:
In the present paper, we introduce the notion of $*$-generalized derivation in near-ring $N$ and investigate some properties involving that of $*$-generalized derivation of a $*$-prime near-ring $N$ which forces $N$ to be a commutative ring. Some properties of generalized semiderivations have also been given in the context of $3$-prime near-rings. Consequently, some well known results have been generalized. Furthermore, we will give examples to demonstrate that the restrictions imposed on the hypothesis of various results are not superfluous.
Keywords:
$3$-prime near-rings, $3$-semiprime near-rings, involution, $*$-derivation, semiderivation, commutativity.
Received: 18.08.2019 Revised: 26.04.2021
Citation:
A. Raji, “Some commutativity criteria for $3$-prime near rings”, Algebra Discrete Math., 32:2 (2021), 280–298
Linking options:
https://www.mathnet.ru/eng/adm822 https://www.mathnet.ru/eng/adm/v32/i2/p280
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Abstract page: | 63 | Full-text PDF : | 20 | References: | 12 |
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