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Pure Mathematics for Theoretical Computer Science

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Online: 2995-3162
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Pure Mathematics for Theoretical Computer Science
Full Length Article

Volume 2Issue 2PP: 30-34 • 2023

On 2-Commutative Derivations of Semi-prime Rings

Othman Al-basheer 1*
1Sudan University of Science and Technology, Faculty of Science, Khartoum, Sudan
* Corresponding Author.
Received: January 26, 2023 Revised: April 14, 2023 Accepted: September 28, 2023

Abstract

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.

Keywords

ring semi-prime ring commutative ring derivation

References

[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.

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Al-basheer, Othman. "On 2-Commutative Derivations of Semi-prime Rings." Pure Mathematics for Theoretical Computer Science, vol. Volume 2, no. Issue 2, 2023, pp. 30-34. DOI: https://doi.org/10.54216/PMTCS.020203
Al-basheer, O. (2023). On 2-Commutative Derivations of Semi-prime Rings. Pure Mathematics for Theoretical Computer Science, Volume 2(Issue 2), 30-34. DOI: https://doi.org/10.54216/PMTCS.020203
Al-basheer, Othman. "On 2-Commutative Derivations of Semi-prime Rings." Pure Mathematics for Theoretical Computer Science Volume 2, no. Issue 2 (2023): 30-34. DOI: https://doi.org/10.54216/PMTCS.020203
Al-basheer, O. (2023) 'On 2-Commutative Derivations of Semi-prime Rings', Pure Mathematics for Theoretical Computer Science, Volume 2(Issue 2), pp. 30-34. DOI: https://doi.org/10.54216/PMTCS.020203
Al-basheer O. On 2-Commutative Derivations of Semi-prime Rings. Pure Mathematics for Theoretical Computer Science. 2023;Volume 2(Issue 2):30-34. DOI: https://doi.org/10.54216/PMTCS.020203
O. Al-basheer, "On 2-Commutative Derivations of Semi-prime Rings," Pure Mathematics for Theoretical Computer Science, vol. Volume 2, no. Issue 2, pp. 30-34, 2023. DOI: https://doi.org/10.54216/PMTCS.020203
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