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Structure of $3$-prime near-rings satisfying some identities
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In this paper, we investigate commutativity of $3$-prime near-rings $\mathcal{N}$ in which $(1, \alpha)$-derivations satisfy certain algebraic identities. Some well-known results characterizing commutativity of $3$-prime near-rings have been generalized. Furthermore, we give some examples show that the restriction imposed on the hypothesis is not superfluous.
Abstract
In this paper, we investigate commutativity of $3$-prime near-rings $\mathcal{N}$ in which $(1, \alpha)$-derivations satisfy certain algebraic identities. Some well-known results characterizing commutativity of $3$-prime near-rings have been generalized. Furthermore, we give some examples show that the restriction imposed on the hypothesis is not superfluous.
참고문헌 (11)
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- H. E. Bell, "Semigroup ideals and commutativity in 3-prime near rings", Comm. Algebra, 43(5), pp.1757~1770 (2015)
- H. E. Bell, "On derivations in near-rings, in Near-rings and near-elds (Tübingen, 1985), 31-35", North-Holland Math. Stud, 137 (1987), North-Holland
- A. Boua, "Semiderivations satisfying certain algebraic identities on prime near-rings", Asian-Eur. J. Math, 6(3), pp.8~ (2013)
- Ö. Gölbasi, "Results on prime near-ring with (σ, τ)-derivation", Math. J. Okayama Univ, 46, pp.1~7 (2004)
- A. A. M. Kamal, "σ-derivations on prime near-rings", Tamkang J. Math, 32(2), pp.89~93 (2001)
- G. Pilz, "Near-Rings", pp.1983, North Holland
- M. S. Samman, "Two sided α-derivations in з-prime near-rings", Rocky Mountain J. Math, 46(4), pp.1379~1393 (2016)
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관련 논문AI추천
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