Generalized skew-derivations acting on multilinear polynomial in prime rings

References

• Beidar, K. I., Martindale, III, W. S., Mikhalev, A. V. (1996). Rings with Generalized Identities. Pure and Applied Mathematics. New York: Dekker.
   Google Scholar
• Chandrashekhar, A., Tiwari, S. K. (2020). A note on generalized derivations as a Jordan homomorphisms. Bull. Korean Math. Soc. 57(3):709–737.
   Web of Science ®Google Scholar
• Bell, H. E., Kappe, L. C. (1989). Rings in which derivations satisfy certain algebraic conditions. Acta Math. Hungar. 53(3–4):339–346. DOI: 10.1007/BF01953371.
   Web of Science ®Google Scholar
• Carini, L., De Filippis, V., Scudo, G. (2016). Identities with product of generalized skew derivations on multilinear polynomials. Commun. Algebra 44(7):3122–3138. DOI: 10.1080/00927872.2015.1027354.
   Web of Science ®Google Scholar
• Chang, J. C. (2003). On the identity h(x)=af(x)+g(x)b. Taiwanese J. Math. 7(1):103–113.
   Web of Science ®Google Scholar
• Chuang, C. L. (1988). GPIs having coefficients in Utumi quotient rings. Proc. Amer. Math. Soc. 103:723–728. DOI: 10.1090/S0002-9939-1988-0947646-4.
   Web of Science ®Google Scholar
• Chuang, C. L. (1992). Differential identities with automorphisms and antiautomorphisms I. J. Algebra 149:371–404. DOI: 10.1016/0021-8693(92)90023-F.
   Web of Science ®Google Scholar
• Chuang, C. L. (2000). Identities with skew derivations. J. Algebra 224(2):292–335. DOI: 10.1006/jabr.1999.8052.
   Web of Science ®Google Scholar
• Chuang, C. L. (1993). Differential identities with automorphisms and antiautomorphisms II. J. Algebra 160(1): 130–171. DOI: 10.1006/jabr.1993.1181.
   Web of Science ®Google Scholar
• Chuang, C. L., Lee, T. K. (2005). Identities with a single skew derivation. J. Algebra 288(1):59–77. DOI: 10.1016/j.jalgebra.2003.12.032.
   Web of Science ®Google Scholar
• De Filippis, V. (2009). Generalized derivations as Jordan homomorphisms on Lie ideals and right ideals. Acta Math. Sinica 25(12):1965–1974. DOI: 10.1007/s10114-009-7343-0.
   Web of Science ®Google Scholar
• De Filippis, V. (2015). Generalized skew Derivations as Jordan Homomorphisms on multilinear polynomials. J. Korean Math. Soc. 52(1):191–207. DOI: 10.4134/JKMS.2015.52.1.191.
   Web of Science ®Google Scholar
• De Filippis, V., Dhara, B. (2019). Generalized skew-derivations and generalization of homomorphism maps in prime rings. Commun. Algebra 47(8):3154–3169. DOI: 10.1080/00927872.2018.1552285.
   Web of Science ®Google Scholar
• De Filippis, V., Di Vincenzo, O. M. (2012). Vanishing derivations and centralizers of generalized derivations on multilinear polynomials. Commun. Algebra 40:1918–1932. DOI: 10.1080/00927872.2011.553859.
   Web of Science ®Google Scholar
• De Filippis, V., Scudo, G., Wei, F. (2021). b-Generalized skew derivations on multilinear polynomials in prime rings. In: Di Vincenzo, O. M., Giambruno, A., eds. Polynomial Identities in Algebras. Cham: Springer, pp. 109–138.
   Google Scholar
• Dhara, B., Argaç, N. (2016). Generalized derivations acting on multilinear polynomials in prime rings and Banach algebras. Commun. Math. Stat. 4(1):39–54. DOI: 10.1007/s40304-015-0073-y.
   Web of Science ®Google Scholar
• Dhara, B. (2018). Generalized derivations acting on multilinear polynomials in prime rings. Czechoslovak Math. J. 68:95–119. DOI: 10.21136/CMJ.2017.0352-16.
   Web of Science ®Google Scholar
• Dhara, B., De Filippis, V., Sandhu, G. S. (2022). Generalized skew-derivations as generalizations of Jordan homomorphisms in prime rings. Commun. Algebra 50(11):5016–5032. DOI: 10.1080/00927872.2022.2080836.
   Web of Science ®Google Scholar
• Erickson, T. S., Martindale III, W. S., Osborn J. M. (1975). Prime nonassociative algebras. Pac. J. Math. 60:49–63. DOI: 10.2140/pjm.1975.60.49.
   Web of Science ®Google Scholar
• Faith, C., Utumi, Y. (1963). On a new proof of Litoff’s theorem. Acta Math. Acad. Sci. Hung. 14:369–371. DOI: 10.1007/BF01895723.
   Google Scholar
• Herstein, I. N. (1969). Topics in Ring Theory. Chicago: University of Chicago Press.
   Google Scholar
• Jacobson, N. (1964). Structure of Rings. American Mathematical Society Colloquium Publications, Vol. 37. Providence, RI: American Mathematical Society.
   Google Scholar
• Lee, P. H., Lee, T. K. (1996). Derivations with Engel conditions on multilinear polynomials. Proc. Amer. Math. Soc. 124(9):2625–2629. DOI: 10.1090/S0002-9939-96-03351-5.
   Web of Science ®Google Scholar
• Lee, T. K. (1992). Semiprime rings with differential identities. Bull. Inst. Math. Acad. Sinica. 20:27–38.
   Google Scholar
• Leron, U. (1975). Nil and power central polynomials in rings. Trans. Amer. Math. Soc. 202:97–103. DOI: 10.1090/S0002-9947-1975-0354764-6.
   Web of Science ®Google Scholar
• Martindale III, W. S. (1969). Prime rings satisfying a generalized polynomial identity. J. Algebra. 12:576–584. DOI: 10.1016/0021-8693(69)90029-5.
   Web of Science ®Google Scholar
• Rehman, N. (2004). On generalized derivations as homomorphisms and anti-homomorphisms. Glas. Mat. III ser.39(1):27–30. DOI: 10.3336/gm.39.1.03.
   Google Scholar
• Tiwari, S. K., Prajapati, B. (2019). Generalized derivations act as a Jordan homomorphism on multilinear polynomials. Commun. Algebra 47(7):2777–2797. DOI: 10.1080/00927872.2018.1539174.
   Web of Science ®Google Scholar
• Tiwari, S. K. (2018). Generalized derivations with multilinear polynomials in prime rings. Commun. Algebra 46:5356–5372. DOI: 10.1080/00927872.2018.1468899.
   Web of Science ®Google Scholar
• Tiwari, S. K. (2022). Product and commuting generalized derivations in prime rings. Rendiconti del Circolo Matematico di Palermo 2:1–21.
   Google Scholar
• Wang, Y. (2006). Generalized derivations with power-central values on multilinear polynomials. Algebra Colloq. 13(3):405–410. DOI: 10.1142/S1005386706000344.
   Web of Science ®Google Scholar
• Wang, Y., You, H. (2007). Derivations as homomorphisms or anti-homomorphisms on Lie ideals. Acta Math. Sinica 32(6):1149–1152. DOI: 10.1007/s10114-005-0840-x.
   Google Scholar