Product of generalized derivations of order 2 with derivations acting on multilinear polynomials with centralizing conditions
Resumo
Let R be a prime ring with char(R) 6= 2. Suppose that f(x1,... , xn) be a noncentral multilinear polynomial over C, G be nonzero generalized derivation of R and d a nonzero derivation of R. In this paper we describe all possible forms of G in the given case.
Downloads
Referências
Argaç, N., and De Filippis, V., Actions of generaliged derivations on multilinear polynomials in prime rings, Algebra Colloq. 18 (Spec 1) (2011), 955-964.
Beidar, K. I., Martimdale III W. S., and Mikhalev, A. V., Rings with generalized identities, Pure and Applied Math., 196, Marcel Dekker, New York, 1996.
Carini, L., De Filippis, V., and Scudo, G., Identites with product of generalized derivations of primr rings, Algebra Colloq. 20 (2013), 711-720.
Chuang, C. L., GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103 (3) (1988), 723-728.
Demir, Ç., and Argaç, N., Prime rings with generalized derivations on right ideals, Algebra Colloq. 18 (2011), 987-998.
Dhara B., and De Filippis, V., Co-commutators with generalized derivations in prime and semiprime rings, Publ. Math. Debrecen 85(3-4) (2014), 339360.
Dhara, B., Kar, S., and Das, P., Pair of generalized derivations acting on multilinear polynomials in prime rings, Hacet. J. Math. Stat. 49 (2) (2020), 740-753.
Brešar, M., On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), 89-93.
Erickson, T. S., Martindale III, W. S., and Osborn, J. M., Prime nonassociative algebras, Pacific J. Math. 60 (1975), 49-63.
Eroˇglu, M. P., and Argaç, N., On identities with composition of generalized derivations, Canad. Math. Bull. 60(4) (2017), 721-735.
De Filippis, V., Product of generalized derivations on polynomials in prime rings, Collectanea Mathematica 61(3) (2010), 303-322.
De Filippis, V., and Dhara, B., Generalized derivations on right ideals and polynomials in prime rings, Southeast Asian Bull. Math. 38 (2014), 341-357.
Faith, C., and Utumi, Y., On a new proof of Litoff’s theorem, Acta Math. Acad. Sci. Hung. 14 (1963), 369-371.
Fosner, M., Vukman, J., Identities with generalized derivations in prime rings, Mediterr. J. Math. 9 (2012), 847-863.
Jacobson, N., Structure of rings, Amer. Math. Soc. Colloq. Pub., 37, Amer. Math. Soc., Providence, RI, 1964.
Kharchenko, V. K., Differential identity of prime rings, Algebra and Logic 17 (1978), 155-168.
Lee, T. K., Generalized derivations of left faithful rings, Comm. Algebra 27 (8) (1999), 4057-4073.
Lee, T. K., Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica 20 (1) (1992), 27-38.
Lee, T. K., and Shiue, W.K., Derivations cocentralizing polynomials, Taiwanese J. Math. 2 (4) (1998), 457-467.
Leron, U., Nil and power central polynomials in rings, Trans. Amer. Math. Soc. 202 (1975), 97-103.
Martindale III, W. S., Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576-584.
Posner, E. C., Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100.
Tiwari, S. K., Identities with Generalized Derivations and Multilinear Polynomials, Bull. Iranian Math. Soc. 46 (2020), 425-440.
Yadav, V. K., Identities involving generalized derivations in prime rings, Rend. Circ. Mat. Palermo, II. Ser. 71 (2022), 259-270.
Copyright (c) 2024 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
