Yarıasal Halkaların Lie İdealleri Üzerinde Bazı Değişmelilik Teoremleri

Year 2020, Volume: 10 Issue: 2, 548 - 556, 30.12.2020

Zeliha Bedir , Öznur Gölbaşı

https://doi.org/10.37094/adyujsci.638265

Abstract

Bu çalışmada, 2 −torsion free bir 𝑅 yarıasal halkasının kare kapalı merkezi olmayan bir 𝑈 Lie idealinin, halkanın sıfırdan farklı bir idealini kapsadığı gösterilecektir. Ayrıca bu sonuçla, yarı asal halkaların Lie ideallerinin çarpımsal genelleştirilmiş türevleri üzerine bazı teoremler genelleştirilecektir.

Keywords

Yarıasal halka, Lie ideal, Çarpımsal genelleştirilmiş türev

Some Commutativity Theorems on Lie Ideals of Semiprime Rings

Abstract

In this paper, we show that any 𝑈 noncentral square closed Lie ideal of a 2 −torsion free semiprime ring 𝑅 contains a nonzero ideal. With this result, some theorems will be extended on the multiplicative generalized derivations of Lie ideals of semiprime rings.

Keywords

semiprime ring, Lie ideal, multiplicative generalized derivation

References

• [1] Bresar, M., On the distance of the composition of two derivations to be the generalized derivations, The Glasgow Mathematical Journal, 33, 89-93, 1991.
• [2] Posner, E.C., Derivations in Prime Rings, Proceedings of the American Mathematical Society, 8, 1093-1100, 1957.
• [3] Herstein, I.N., Topics in ring theory, University of Chicago Press, 1969.
• [4] Martindale, W.S., When are multiplicative maps additive, Proceedings of the American Mathematical Society, 21, 695-698, 1969.
• [5] Daif, M.N., When is a multiplicative derivation additive, International Journal of Mathematics and Mathematical Sciences, 14(3), 615-618, 1991.
• [6] Goldman, H., Semrl, P ., Multiplicative derivations on C(X), Monatshefte für Mathematik, 121(3), 189-197, 1969.
• [7] Daif, M. N., Tammam El-Sayiad, M.S., Multiplicative generalized derivations which are additive, East-West Journal of Mathematics, 9, 31-37, 1997.
• [8] Dhara, B., Ali, S., On multiplicative (generalized)-derivation in prime and semiprime rings, Aequationes mathematicae, 86, 65-79, 2013.
• [9] Eremita, D., Ilisevic, D., On additivity of centralizers, Bulletin of the Australian Mathematical Society, 74, 177-184, 2006.
• [10] Ali, A., Dhara, B., Ali, F., Multiplicative (generalized)-derivations and left ideals in semiprime rings, Hacettepe Journal of Mathematics and Statistics, 44, 1293-1306, 2015.
• [11] Ali, S., Dhara, B., Dar, N.A., Khan, A.N., On Lie ideals with multiplicative (generalized)-derivations in prime and semiprime rings, Beiträge zur Algebra und Geometrie, 56, 325-337, 2015.
• [12] Koç, E., Gölbaşı, Ö., Multiplicative generalized derivations on Lie ideals in semiprime rings, Palastine Journal of Mathematics, 6, 219-227, 2017.
• [13] Gölbaşı, Ö., Multiplicative generalized derivations on ideals in semiprime rings, Mathematica Slovaca, 66, 1285-1296, 2016.
• [14] Huang, S., Derivations on Lie ideals of semiprime rings, Gulf Journal of Mathematics, 6(3), 25-32, 2018.
• [15] Samman, M.S., Alyamani, N., Derivations on semiprime ring, International Journal of Pure and Applied Mathematics, 5(4), 469-477, 2003.