21. Dorofeev.G.V., Center of nonassociative rings, Alg I Logika, Vol.12, No.5,1973, Dzhunushaliev.V, A non-associative quantum mechanics,

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1 REFERENCES 1. Adler.S.L, Quaternionic Quantum Mechanics and Quantum Fields, Oxford Univ. Press, New York, Albert A.A., Almost alternative algebras, Portugal math., 8,1949, Albert A.A., Power associative rings, Trans, Amer. Math. Soc. 64,1948, Anderson C.T and Outcalt.D.L, On simple anti-flexible rings, J.Algebra, 10, 1968, Ashaf. M, Quadri.M.A and Zalihsky.D, Some polynomial identities that imply commutativity for rings, Amer.Math.Monthy 95, No.4,1988, Baez.J.C., The Octonions, Bull.Amer.Math.Soc.,39, ,2002,math.ra/ Bars.I and Gunaydin.M., Phys.Rev.D22, 1980, Bell,H.E.and Daif, M.N., On derivation and commutativity in prime rings, Amer.Math.Bull.21,1987, Bell,H.E. and Daif, M.N., On Derivations and Commutativity in prime rings, Acta Math. Hungar., 66(4),1995, Bell, H.E. and Martindale W.S., Centralizing Mappings of sempirime rings, Canada. Math. Bull.21,1987, Bell,H.E. and Martindale, W.S III, Centralizing Mappings of semiprime rings ad. Math.Bull.21,1987, Bell, H.E. and Kappe, L.C., Rings in which derivations satisfy certain algebraic Conditions, Acta Math. Hungar., 53,1989, Benslama.A and Mebarki.N, JHEP, 0002,2000, Bernevig.B.A, Hu.J.P, Toumbas.N and Zhang.S.C, The Eight Dimensional Quantum Hall Effect and the Octonions, phys.rev.lett.91,2003, Boers A.H, On assosymmetric rings, Indag Mathe.N.S.5(1),1994, Celik H.A., On primitive and prime antiflexible rings, J.of Algebra,1972, Daif, M.N., Commutative results for semi prime rings with derivations, Interest J. Math. & Math Sci., 3,1998, Daif, M.N. and Bell, H.E., Remarks on derivations of semiprime rings, Internet. J.Math & Math. Sci., 15,1992, De Medeiros.P and Ramgoolam.S, JHEP, 0503,2005, Dorofeev.G.V., Alternative rings with three generators, Sibirsk. Matem.Zh.4,1963,

2 21. Dorofeev.G.V., Center of nonassociative rings, Alg I Logika, Vol.12, No.5,1973, Dzhunushaliev.V, A non-associative quantum mechanics, to be published in Found. Phys. Lett., hep-th/ Dzhunushaliev.V., Non-perturbative operator quantization of strongly interacting fields, Found.Phys. Lett.16, 2003, Elduqua.A and Myung.H.C, Mutations of alternative algebras, kluwer Ac. Publ, Dordrecht, Gogberashvili.M., Octonionic version of Dirac equations, hep-th/ Gogberashvili.M., Octonionic Geometry, hepth/ Grossman.B., A Three Cocycle in Quantum Mechanics, Phys. Lett. B152,1985, G unaydin.m., Nuovo Cimento, 1973, G unaydin.m and Gursey.F., Phys. Rev., D9, 1974, G ursey Feza and Chia- Hsiung Tze., On the Role of Division, Jordan and Related Algebras in Particle Physics, World Scientific, Singapore, G Ursey Lett.F., J.Math.Phys., 14,1973, Herstein.I.N., A note on derivations, Canad. Math. Bull., 21,1978, Herstein. I.N., A note on rings with central nilpotent elements, Proc. Amer. Math. Soc., 2,1954, Jackiw. R, 3-Cocycle in Mathematics and Physics, Phys. Lett. B152,1985, Jacobs. D.P, Muddana. S.V, Offutt.A.J., A Computer algebra system for nonassociative indentities, Hadronics n Mechanics and nonpotential. 36. Johnsen, Outcalt, Yaqub Jordan.P., An elementary commutativity theorems for rings, Amer.Math.Monthly.75,1968, Joseph.B, Andre.C, Micali.A and Moussa.Q., Derivations in power associative algebras, Discrete and continuous Dynanical systems series Vol.4, No.6,2011, Khan. M.S.S., A note on commutativity of nonassociative rings, Inter.J.Math.Sci.Vol.23, No 3,2000, Kleinfeld E., Assosymmetric rings, Proc. Amer. Math. Soc., 8, 1957, Kleinfeld E., Generalization of alternative rings I, J. Algebra, 18,1974, Kleinfeld E., Generalization of alternative rings II, J. Algebra, 18, 1971, Kleinfeld E., On a class of right alternative rings, Math.Z., 87, 1965,

3 43. Kleinfeld E., Privitive alternative rings and semisimplicity, Am. J. Math., 77, 1953, Kleinfeld E., Kleinfeld.M.H, and Kosier.F., The structure of generalized accessible rings, Bull. Amer. Math. Soc., 75, 1969, Kokoris. L.A., On rings of (γ, δ) type, Proc. Amer. Math. Soc,9,1958, Kosier. F., On a class of nonflexible algebras, Trans. Amer. Math. Soc., 102,1962, Ko.Y.S., On mutations of prime associative algebras, Comm. Korean Math. Soc.9,1994, Kugo. T and Townsend.P.K., Supersymmetry and the division algebras, Nucl. Phys. B221, 1983, Lohmus. J, Pall.E and Sorgsepp.L., Acta Appl. Math, 50, 1998, Majid. S., Gauge theory on nonassociative spaces, math. Qa/ Manogue. C.A. and Dray.T., Mod. Phys. Lett. A 14,99,1999[arXiv:hepth/ ]. 52. Manogue C.A. and Sudbery., Phys. Rev. D40., 1989, Mates Bresar., Centralizing mappings and Derivations in Prime rings, J of Algebra 156., 1993, Morita.K., Prog. Theor., Phys., 1981, Nadeem-Ur-Rehman., On commutative of rings with generalized derivations, Math. J. Okayama Univ. 44, 2002, Nesterov. A.I., Three-cocycles, nonassociative gauge transformations and Dirac s monopole, Phys. Lett. A328., 2004, Nesterov. A.I and Sabinin. L.V., Nonassociative geometry: Towards discrete structure of spacetime, Phys. Rev. D62, 2000, Ng Seong Nam, Right nucleus in right alternative algebras, J. London Math., 21(2), 1980, Oznur.G and Emine.K., Generalized derivations on lie ideals in prime rings, Turk J. Math 35,2011, Oznur. G and Emine. K., Notes on commutativity of prime rings with generalized derivation, Commun.Fac.Sci.Univ.Ank.Series A, Volume 58, Number 2, page 39-46,2009, ISSN Pascual Jordan John von Neumann, Eugene Wigner, On a algebraic generalization of the quantum mechanical formalism, Ann. Math. 35,1934, Pati J.C, Salam.A and Strathdee.J, Nucl. Phys. B 185,1981,

4 63. Quadri.M.A, Khan M.S and Rehman.N., Generalized derivations and commutativity of prime rings, Indian J. Pure appl. Math, 34(9), 2003, Quadri M.A, Shadad.Khan. M and Rehman.N., Generalized derivations and commutativity of prime rigs, Indian J.Pure Appl. Math.34(9), 2003, Rodabaugh. D., A generalization of the flexible law, Trans. Amer. Math. Soc., 1965, Rodabaugh. D., On semisimple antiflexible algebras, Portugal Math., 26,1967, Ramgoolam.S., JHEP, 0403,2004, Schafer. R., Introduction to Non-Associative, Algebras(Dover, New York, 1995). 69. Schafer. R.D., An introduction to nonassociative algebras, Acadamic Press. New York, Schafer. R.D., On generalized standard algebras., Proc. Nat. Acad. Sci.USA, 60,1968, Shraf.M, Quadri. M.A and Zelinsky.D., Some polynomial identities that imply commutativity for rings, Amer. Math, Mothly95,1988, no-4, Slater. M., Nucleus and center in alternative rings, Journal of Algebra, 1967, Smolin. L., Octonions, Jordan algebras and exceptional groups, Springer Monographs in Math(Berlin, 2000), arxiv:hep-th/ Springer T.A and Beldkamp F.D., Octonions, Jordan algebras and exceptional groups, Springer Monographs in Math(Berlin, 2000), arxiv:hepth/ Stephen L.Adler., Quaternionic Quantum Mechanics and Quantum Fields, Oxford University Press, New York, Sterling.N., Rings satisfying (x,y,z) = (y,z,x), Can J. Math., 20, 1968, Suh.I.T., Prime non associative rings with a special derivation, Amer. Math. Soc., 14, 1993, Susumo Okubo., Introduction to Octonion and Other Non-Associative Algebras in Physics, Cambrodge University Press, Cambridge, Suvarna. K and Jayalakshmi.K., On left nucleus in the prime left alternative rigns., P.A.J. Math, Vol4, No.2, 2010, Suvarna. K and Jayalakshmi.K., Idempotents in the nucleus of an assosymmetric ring, IJMSEA, ISSN , Vol.5 No.I, 2011,

5 81. Suvarna. K and Jayalakshmi.K., On the nucleus of prime assosymmetric ring J. Pure & Appl. Phys, vol.22, No.1, 2010, Suvarna.K and Madhavi. T., Commutativity of semiprime rings with derivations, Inter.J, of Math, Sci. and Engg. Appls, ISSN , Vol. 6, 2012, Thedy.A., right alternative rings, J.Algebra., 37,1975, Yen.C.T., Nonassociative rings with special derivations, Tankanga J. Math., 1995, Yuanchun. G., Some commutativity theorems of rings, Acta. Sci. Natur. Univ. Jilin 3,1983, Yuji ko bayashi., The identity (xy) n = x n y n and commutativity of rings, Math. J.Okayama. Univ.23, 1981,

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