Geodesic
Some commutativity criteria for $3$-prime near rings
Algebra and discrete mathematics, Tome 32 (2021) no. 2, pp. 280-298

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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. 
@article{ADM_2021_32_2_a9,
     author = {A. Raji},
     title = {Some commutativity criteria for $3$-prime near rings},
     journal = {Algebra and discrete mathematics},
     pages = {280--298},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a9/}
}
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A. Raji. Some commutativity criteria for $3$-prime near rings. Algebra and discrete mathematics, Tome 32 (2021) no. 2, pp. 280-298. http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a9/