Volume 4 • Issue 1 • PP: 22-34 • 2024
Orthogonal Semi derivations on Semi prime Γ-Semi rings
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In this paper, we introduce the notion of orthogonal semi derivations on Γ-semi rings. Some characterizations of semiprime Γ-semirings are obtained by means of orthogonal semi derivations and obtained necessary and sufficient conditions for two semi derivations to be orthogonal.
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References
[1] Nobusawa N. On a generalization of the ring theory 1964.
[2] Sen MK. Proceeding of International Conference on Algebra and its Applications 1981.
[3] Lehmer DH. A ternary analogue of abelian groups. Am J Math 1932;54:329–38.
[4] Lister WG. Ternary rings. Trans Am Math Soc 1971;154:37–55.
[5] Dutta TK, Kar S. On regular ternary semirings. Adv. Algebr. Proc. ICM Satell. Conf. Algebr. Relat. Top. World Sci., 2003, p. 343–55.
[6] Rao MMK. Γ-semirings-I. Southeast Asian Bull Math 1995;19:49–54.
[7] Murali Krishna Rao M. Prime bi-interior ideals of Γ-semirings. J Hyperstructures 2023;11:20–30.
[8] Bergen J. Derivations in prime rings. Can Math Bull 1983;26:267–70.
[9] Brešar M, Vukman J. On some additive mappings in rings with involution. Aequationes Math 1989;38:178–85.
[10] Bresar M. Orthogonal derivations and extension of a theorem of Posner. Rad Math 1989;5:237–46.
[11] Posner EC. Derivations in prime rings. Proc Am Math Soc 1957;8:1093–100.
[12] Chang J-C. On semi-derivations of prime rings. Chinese J Math 1984:255–62.
[13] Chuang C-L. On the structure of semiderivations in prime rings. Proc Am Math Soc 1990;108:867–9.
[14] Firat A. Some results for semi derivations of prime rings. Int J Pure Appl Math 2006;28:363.
[15] Ali S, Khan MS. On orthogonal (σ, τ)-derivations in semiprime Γ-rings. Int Electron J Algebr 2013;13:23–39.
[16] Hamil SA. Commutativity of Prime Γ-Semirings with Derivations and Generalized Derivations. J. Phys. Conf. Ser., vol. 1804, IOP Publishing; 2021, p. 12091.
[17] Rasheed MK, Hameed FA, Majeed AH. On Generalized (α, β) Derivation on Prime Semirings. J. Phys. Conf. Ser., vol. 1591, IOP Publishing; 2020, p. 12080.
[18] Rasheed MK, Majeed AH. Developing an improved grey prediction model for application to electricity consumption prediction: toward enhanced model accuracy. J. Phys. Conf. Ser., vol. 1362, IOP Publishing; 2019, p. 12137.
[19] Ibraheem RKH, Majeed AH. On Lie Structure in Semiprime Inverse Semirings. Iraqi J Sci 2019:2711–8.
[20] Dey KK, Paul AC, Rakhimov IS. Semiprime gamma rings with orthogonal reverse derivations. Int J Pure Appl Math 2013;83:233–45.
[21] Sindhu KK, Murugesan R, Namasivayam P. Orthogonl Semiderivtions on Semiprime Semirings. Int Organ Sci Res J Math 2015;11:18–24.
[22] Venkateswarlu B, Rao MMK, Narayana YA. ORTHOGONAL DERIVATIONS ON Γ− SEMIRINGS n.d.
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