2995-3162ISSN (Online)
Volume 2 , Issue 2 , PP: 30-34, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
Othman Al-Basheer 1 *
Doi: https://doi.org/10.54216/PMTCS.020203
The main purpose of this paper is to study some results concerning the generalized derivation D defined on semi-prime ring R, we obtain a derivation d which commuting and 2-commuting on R. Also, we present many examples to clarify the validity of our work.
ring , semi-prime ring , commutative ring , derivation
[1] M. Ashraf, Asma Ali and Rekha Rani, On generalized derivations of prime rings , Southeast Asian Bulletin of Mathematics , 29(2005),669-675.
[2] M.A. Quadri, M. Shadab Khan and N. Rehman,Generalized derivations and commutativity of prime rings, Indian Journal Pure Apply Mthathematics,34(9)(2003),1393-1396.
[3]N.Divinsky, Oncommuting automorphisms of rings, Transactions of
Royal Society of Canada, Section III.(3)49(1955), 19-22.
[4]E.C.Posner, Derivations in prime rings. Proceedings of the American Mathematical Society,8(1957),1093-1100.
[5] J.Luch. A note on commuting automorphisms of rings, American Mathematical. Monthly77(1970),61-62.
[6] J.H.Mayne, Centraliziting automorphisms of prime rings, Canadian Mathematical Bulletin19(1976), No.1,113- 115.
[7] L.O.Chung and J.Luh,On semicommuting automorphisms of rings, Canadian Mathematical Bulletin, 21(1)(1978),13-16.
[8]H.EBell and,W.S MatindaleIII, Centralizing mappings of semiprime rings, Canadian Mathematical Bulletin.,30(1) (1987), 92-101.
[9]M. Bresar, On the distance of the composition of two derivation to generalized derivations, Glasgow Mathematical Journal ,33(1991), 89-93.
[10]Q.Deng and H.E.Bell, On derivations and commutativity in semiprime rings, Communications in Algebra ,23(1995),3705-3713.
[11] B.Hvala, Generalized derivations in rings, Communications in Algebra, 26(4)(1998), 1147-1166.
[12] A.H. Majeed and Mehsin Jabel Attya , Some results of orthogonal generalized derivations on semiprime rings, Scientific Conference of College of Sciences , Al-Muthana Univ.,2007,90.
[13]Mehsin derivations Jabel,On of generalized semiprime rings, International Journal of Algebra,no.12,4(2010),591-598.
[14] Mehsin Jabel, On orthogonal generalized derivations of semiprime
rings, International Mathematical Forum, 5( 2010),no. 28, 1377 – 1384.
[15] L. Moln'ar,On centralizers of H*- algebra, Publicationes Mathematicae Debrecen, 46(1-2)(1995),89-95.
[16] Muhammad A.C. and S.,S. Mohammed, Generalized inverses of
centralizer of semiprime rings , Aequations Mathematicae , 71(2006) ,1-7.
[17]Muhammad A.and A.B. Thaheem, Anote on a pair of derivations of semiprime rings, International Journal of Mathematics and Mathematical Sciences, 39(2004), 2097-2102.
[18] A.B. Thaheem, On some properties of derivations on semiprime rings, Southeast Asian Bulletin of Mathematics, 29(2005),1143-1152.
[19] J.Vukman, and Kosi–Ulbl,I.,An equation related to centralizers in
semiprime rings, Glasnik Matematicki,38(58)(2003), 253-261.
[20] J.Vukman,An identity related to centralizers Commentations in semiprime rings, Mathematicae Universitatis Carolinae 40(1999),447 456.
[21] J.Vukman, Centralizers on semiprime rings, Commentations Mathematicae Universitatis Carolinae 38(1997),231-240.
[22] J.Vukman, Centralizers on semiprime rings, Commentations Mathematicae Universitatis Carolinae ,42(2001), 237- 245.
[23] J.Vukman, Identities with derivations and automorphisms on semiprime rings, International Journal of Mathematics and Mathematical Sciences ,7(2005) ,1031-1038.
[24] B.Zalar, On centralizers of semiprime rings, Commentations Mathematicae Universitatis Carolinae,32(4)(1991),609- 614.
