Symmetric Higher Bi-Left (Right)Centerlizerhomo of Γ Ring
DOI:
https://doi.org/10.32628/IJSRSET2512539Keywords:
Γ-ring, symmetric higher bi-left (right) centerlizerhomomorphism (SHBL(r.r)CH), jointly symmetric higher bi-left (right) centerlizerhomomorphism (JSHBL(r.r)CH), jointly totally symmetric higher bi-left (right) centerlizerhomomorphism (JTSHBL(r.r)CH), homomorphism, ring theory, structure-preserving maps, generalizationAbstract
This chapter investigates the structural properties of symmetric higher bi-left (right) centerlizerhomomorphisms (SHBL(r.r)CH) within the framework of Γ-rings. In the first section, the notions of SHBL(r.r)CH, jointly symmetric higher bi-left (right) centerlizerhomomorphisms (JSHBL(r.r)CH), and jointly totally symmetric higher bi-left (right) centerlizerhomomorphisms (JTSHBL(r.r)CH) are introduced and rigorously examined. The interrelations among these mappings are explored in depth, leading to the significant result that every SHBL(r.r)CH of a Γ-ring is also a JTSHBL(r.r)CH. The second section of the chapter generalizes these findings to broader classes of Γ-rings, providing a unified framework for future research in this area. These developments contribute to a deeper understanding of homomorphic mappings in Γ-ring theory and their symmetric structures.
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References
J.S. Aneed,, S.M. Salih, "Orthogonal generalized higher symmetric reverse bi-derivations and generalized higher symmetric bi-derivations on semiprime Γ-rings ", AipConference Proceedings, Volume 3036, Issue 1,pp. 040041, 2024.
O. Beqiri “Homomorphism in weakly Γ-Ring” Interdisciplinary Journal of Research and Development, Vol. 10, no. 2,pp. 78-81, (2023)
W.E. Beqiri,”on the Γ-ring of Nobusawa” pacific journal of mathmatices ,18(3),pp.411-422,1966
A. K. Faraj, A. H. Majeed, Haetinger, C., & N.-u. Rehman,(2014). On Generalized Jordan Higher Homomorphisms. Palestine Journal of Mathematics, 3(Special Issue 1), PP. 406–421.
O. Faruk and Md .M. Rahman ,"Generalized Jordan Right Derivations on Prime and Semiprime Γ-rings ", Journal of Mechanics of Continua and Mathematical Sciences,14(4), pp.268 - 280,2
I.N. Herstein, "Topics in Ring Theory", Ed. The University of Chicago Press, Chicago, 1969
SH.K. S. Husain and K.K. Dey “Homoderivations of − prime -rins” Advances in Mathematics: Scientific Journal, Vol. 10, no. . pp. 83-91, (2021).
Jarullah, R.F Jarullah, S.M. Salih,"A Jordan higher reverse left (resp. right) centralizer on prime Γ-Rings ", Iraqi Journal of Science,Vol. 61, No.9, pp. 2341–2349, 2020.
E.M, Khazal. and S. M. Salih “Jordan centralizerhomo on prime -ring” AIP publishing 2ed International conference of mathematics, applied sciece, information and communication technology 1-2 May, Baghdad, Iraq 2022. AIP Conf. Proc. Vol.2834, Issue 1, 080143 (2023)
M.O, Karim “ Jordan generalized centralizerhomo on prime rings” Journal of Advances in Mathematics, Vol. 21,pp.1-4, 2022.
J. Luh, "On the Theory of Simple Γ- Rings", Michigan Mathematical Journal ,16(1) , pp. 65-75, 1969.
A.H. Mahmood, Salih, S.M. Salih, R.M. Al-Omary, "Jordan Higher ⋆-Left (Accordingly Right)-Centralizers on Prime Rings With Involution" Al-Nahrain J. Sci., 28(2):pp. 189-191, 2025.
N.ur, Rehman and H, Alnoghash. “Identities related to homo-derivation on ideal in prime rings” Journal of Siberian Federal University, Vol. 16,no. 3, pp.370–384, (2023).
Shakir Ali, N. N.Rafiquee1, V. Varshney , and, D. Outdom“Reverse Homoderivations on (Semi)-prime Rings” J. Indones. Math. Soc. Vol. 31, No. 3, pp. 1–13, 2025.
S.M. Salih, H.H. Abd-Ali," Orthogonal Generalized Higher k-Derivation on Semi Prime Γ-Rings" Iraqi Journal of Science, Vol. 64, No. 2, pp. 834–841, 2023.
S.M. Salih and .S.J, Shaker "Orthogonal generalized symmetric higher bi-derivation on semiprime Г- Rings " .Iraqi Journal of science.59(2) , pp.711-723,2018 .
S.M .Salih ; D.M. Hameed, "Jordan permuting 3-left (resp. right) µ-centralizers on prime semi-rings" J. Discrete Math. Sci.& Cryptography, 28(4-A):1221–1226, 2025.
S.M Salih, and N.N Sulaiman , “Jordan Triple Higher Homomorphisms on Prime Rings” raqi Journal of Science, Vol. 61, No. 10, pp: 2671-2680, 2020).
H.J. Thahab, S.M. Salih, "On Jordan Generalized Symmetric Higher Bi-Left (Resp. Right) Centralizers on Prime Г-Rings", Aip Conference Proceedings, Volume 2414, Issue 1, 040073, 2023.
B. Zalar, on centerlizers of semiprime Ring commentmath.university carolinue. 32(4).pp.609-614,1991
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