Geodesic
Left Annihilator of Identities with Generalized Derivations in Prime and Semiprime Rings
Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 69-79.

Voir la notice de l'article provenant de la source Library of Science

Let R be a noncommutative prime ring of char (R) ≠ 2, F a generalized derivation of R associated to the derivation d of R and I a nonzero ideal of R. Let S ⊆ R. The left annihilator of S in R is denoted by lR(S) and defined by lR (S) = x ∈ R | xS = 0. In the present paper, we study the left annihilator of the sets F(x) ◦n F(y)−x ◦n y | x, y ∈ I and F(x) ◦n F(y)−d(x ◦n y) | x, y ∈ I.
Keywords: prime ring, derivation, generalized derivation, extended centroid, Utumi quotient ring 
@article{DMGAA_2021_41_1_a6,
     author = {Rahaman, Md Hamidur},
     title = {Left {Annihilator} of {Identities} with {Generalized} {Derivations} in {Prime} and {Semiprime} {Rings}},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {69--79},
     publisher = {mathdoc},
     volume = {41},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2021_41_1_a6/}
}
TY  - JOUR
AU  - Rahaman, Md Hamidur
TI  - Left Annihilator of Identities with Generalized Derivations in Prime and Semiprime Rings
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2021
SP  - 69
EP  - 79
VL  - 41
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2021_41_1_a6/
LA  - en
ID  - DMGAA_2021_41_1_a6
ER  - 
%0 Journal Article
%A Rahaman, Md Hamidur
%T Left Annihilator of Identities with Generalized Derivations in Prime and Semiprime Rings
%J Discussiones Mathematicae. General Algebra and Applications
%D 2021
%P 69-79
%V 41
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2021_41_1_a6/
%G en
%F DMGAA_2021_41_1_a6
Rahaman, Md Hamidur. Left Annihilator of Identities with Generalized Derivations in Prime and Semiprime Rings. Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 69-79. http://geodesic.mathdoc.fr/item/DMGAA_2021_41_1_a6/

[1] S. Ali and H. Shuliang, On derivations in semiprime rings, Algebra Represent Theor. 15 (2012) 1023–1033. doi:10.1007/s10468-011-9271-9

[2] M. Ashraf, A. Ali and R. Rani, On generalized derivations of prime rings, Southeast Asian Bull. Math. 29 (2005) 669–675.

[3] M. Ashraf and N. Rehman, On commutativity of rings with derivations, Results Math. 42 (2002) 3–8. doi:10.1007/BF03323547

[4] H.E. Bell and N. Rehman, Generalized derivations with commutativity and anti-commutativity conditions, Math. J. Okayama Univ. 49 (2007) 139–147.

[5] H.E. Bell and W.S. Martindale III, Centralizing mappings of semiprime rings, Canad. Math. Bull. 30 (1987) 92–101. doi:10.4153/CMB-1987-014-x

[6] K.I. Beidar, Rings of quotients of semiprime rings, Vestnik Moskow. Univ. Ser. I. Mat. Mekh. (Engl. Transl: Moskow Univ. Math. Bull.) 33 (1978) 36–42.

[7] C.L. Chuang, Hypercentral derivations, J. Algebra 166 (1994) 34–71. doi:10.1006/jabr.1994.1140

[8] C.L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103 (1988) 723–728. doi:10.1090/S0002-9939-1988-0947646-4

[9] B. Dhara, S. Ali and A. Pattanayak, Identities with generalized derivations in semiprime rings, Demonstratio Math. XLVI (2013) 453–460. doi:10.1515/dema-2013-0471

[10] T.S. Erickson, W.S. Martindale III and J.M. Osborn, Prime nonassociative algebras, Pacific J. Math. 60 (1975) 49–63. doi:10.2140/pjm.1975.60.49

[11] I.N. Herstein, Topics in Ring Theorey (The University of Chicago Press, Chicago, 1969).

[12] S. Huang, Generalized derivations of prime rings, Int. J. Math. & Math. Sci. Volume 2007, Article ID 85612, 6 pages. doi:10.1155/2007/85612

[13] N. Jacobson, Structure of rings, Amer. Math. Soc. Colloq. Pub. 37, Amer. Math. Soc. (Providence, RI, 1964).

[14] V.K. Kharchenko, Differential identity of prime rings, Algebra and Logic. 17 (1978) 155–168. doi:10.1007/BF01669313

[15] T.K. Lee, Generalized derivations of left faithful rings, Comm. Algebra 27 (1999) 4057–4073. doi:10.1080/00927879908826682

[16] T.K. Lee, Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica 20 (1992) 27–38.

[17] W.S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969) 576–584. doi:10.1016/0021-8693(69)90029-5

[18] M.A. Raza and N.U. Rehman, On generalized derivation in rings and Banach Algebras, Kragujevac J. Math. 41 (2017) 105–120. doi:10.5937/KgJMath1701105R