Vol2 Paper 21

posted Aug 27, 2018, 12:11 AM by Yaseen Raouf Mohammed   [ updated Sep 4, 2018, 2:14 AM ]

 Adil Kadir Jabbar

 Department of Mathematics, College of Science, University of Sulaimani, Sulaimani-Iraq.

 Farhad Rafiq Krush

 Directorate of Education of Sulaimani- District West.

In this paper some conditions are obtained under which certain elements and certain ideals of a ring R become central elements and central ideals and some other conditions are determined which make a given additive mapping of a centrally semiprime ring as a derivation. Also, certain types of additive mapping have been studied such as, reverse derivations, Jordan derivations and α − derivations and some properties of each one are proved and the relations between them are established.

Semiprime rings, centrally semiprime rings, n − torsion free ring and free actions,derivations, reverse derivations, α − derivations and Jordan centralizers.

[1] M. A. Chaudhry and A. B. Thaheem: A Note on a pair of derivations of semiprime rings, IJMMS, Vol. 39, [2004], PP 2097-2102.
[2] M. N. Daif: On generalized derivations of semiprime rings with involution, International Journal of Algebra, Vol. 1, No. 12, [2007], pp. 551-555.
[3] M. N. Daif and H. E. Bell: Remarks on derivations on semiprime rings, Internat. J. Math. & Math. Sci. ,Vol. 15, No. 1, [1992], pp. 205-206.
[4] M. Fosner and J. Vukman: On some equations in prime rings. Montash. Math. 152, [2007], pp. 135-150.
[5] A. K. Jabbar and A. H. Majeed: On Centrally Semiprime Rings and Centrally Semiprime Near-rings with Derivations, Journal of Kirkuk University, Scientific Studies vol. 3, No.1, [2008], pp.158-168.
[6] A. K. Jabbar: On Centrally Prime Rings and Centrally Prime Near-Rings with Derivations, Ph. D. Thesis, University of Sulaimani, [2007].
[7] Y. S. Jung and K. H. Park: On Generalized (α ,β ) − Derivations and commutativity in Prime Rings, Bull. Korean Math. Soc., Vol. 43, [2006], pp. 101-106.
[8] B. D. Kim: Derivations of semiprime ring and noncommutative Banach algebra, Commun. Korea Math. Soc.17, No. 4, [2002], pp. 607-618.
[9] M. D. Larsen and P. J. McCarthy: Multiplicative Theory of Ideals, Academic Press New York and London [1971].
[10] E. H. Lee, Y. S. Jung and I. S. Chang: Derivations on prime and semi-prime rings, Bull. Korean. Soc.39, No. 3, [2002], pp. 485- 494 .
[11] A. N. Mustafa: On Jordan n-ripple higher derivations and centralized derivations on semiprime rings, M. Sc. Thesis, University of Sulaimani [2007].
[12] M. S. Samman and M. A. Chaudhry: Dependent elements of left centralizer of semiprime rings, The Arabian Journal for Science and Engineering, vol. 33, No. 2A, [2008], p p 313-319 .
[13] M. Samman and N. Alyamani: Derivations and Reverse Derivations in Semiprime Rings, International Math. Fourm, No. 39, [2007], pp.1895-1902.
[14] J. Vukman and I. K. Ulbl: On centralizers of semiprime rings with involution, Studia Scientiarum Mathematicarum Hungarica, 43[1], [2006], pp. 61-67.
[15] J. Vukman and I. K. Ulbl: on dependent elements in rings, UMMS, No. 54, [2004], pp. 2895-2906.
[16] J. Vukman: Jordan left derivations on semiprime rings, Math. J. Okayama Univ. 39, [1997], pp. 1-6 .
[17] M. S. Yenigul and N. Argac: on prime and semiprime rings with α − derivations, Tr. J. of Math. ,18, [1994], pp. 280-284. 236
[18] B. Zalar: On Centralizers of Semiprime Rings, Comment. Math. Univ. Caroline 32,4, [1991], pp. 609-614.

View All Artical