Some identities in rings and near-rings with derivations. (English) Zbl 1488.16145
Summary: In the present paper we investigate commutativity in prime rings and \(3\)-prime near-rings admitting a generalized derivation satisfying certain algebraic identities. Some well-known results characterizing commutativity of prime rings and \(3\)-prime near-rings have been generalized.
MSC:
| 16Y30 | Near-rings |
| 16N60 | Prime and semiprime associative rings |
| 16W25 | Derivations, actions of Lie algebras |
References:
| [1] | M. Ashraf, A. Ali and S. Ali, (σ, τ)-derivations on prime near-rings, Arch. Math. (Brno)40 (2004), 281-286. · Zbl 1114.16040 |
| [2] | M. Ashraf and S. Ali,On(σ, τ)-derivations of prime near-rings II, Sarajevo J. Math.4(2008), 23-30. · Zbl 1169.16028 |
| [3] | D. Basudeb,Remarks on generalized derivations in prime and semiprime rings, Int. J. Math. Math. Sci. (2010), Article ID 646587. · Zbl 1220.16030 |
| [4] | K. I. Beidar, Y. Fong and X. K. Wang,Posner and Herstein theorems for derivations of3-prime near-rings, Comm. Algebra24(1996), 1581-1589. · Zbl 0849.16039 |
| [5] | H. E. Bell,On Derivations in Near-Rings II, Kluwer Academic Publishers, Amsterdam, 1997. · Zbl 0911.16026 |
| [6] | H. E. Bell and G. Mason,On Derivations in Near-Ring in Near-Rings and Near-Fields, NorthHolland, Amsterdam, 1987, 31-35. · Zbl 0619.16024 |
| [7] | H. E . Bell and G. Mason,On derivations in near-rings and rings, Math. J. Okayama Univ.34 (1992), 135-144. · Zbl 0810.16042 |
| [8] | H. E. Bell, A. Boua and L. Oukhtite,On derivations of prime near-rings, Afr. Diaspora J. Math. 14(1) (2012), 65-72. · Zbl 1280.16047 |
| [9] | A. Boua, A. Y. Abdelwanis and A. Chillali,Some commutativity theorems for near-rings with left multipliers, Kragujevac J. Math.44(2) (2020), 205-216. · Zbl 1488.16143 |
| [10] | M. Brešar,On the distance of composition of two derivations to the generalized derivations, Glasg. Math. J.33(1991), 89-93. · Zbl 0731.47037 |
| [11] | M. N. Daif and H. E. Bell,Remarks on derivations on semiprime rings, Int. J. Math. Math. Sci. 15(1992), 205-206. · Zbl 0746.16029 |
| [12] | Ö. Gölbasi and E. Koc,Notes on commutativity of prime rings with generalized derivation, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.58(2009), 39-46. · Zbl 1207.16046 |
| [13] | Ö. Gölbasi and E. Koc,Some commutativity theorems of prime rings with generalized(σ, τ)derivation, Commun. Korean Math. Soc.26(2011), 445-454. · Zbl 1234.16029 |
| [14] | Ö. Gölbasi,Notes on prime near-rings with generalized derivation, Southeast Asian Bull. Math. 30(2006), 49-54. · Zbl 1117.16033 |
| [15] | A. A. M. Kamal,σ-Derivations on prime near-rings, Tamkang J. Math.32(2001), 89-93. · Zbl 0992.16035 |
| [16] | M. A. Quadri, M. Shadab Khan and N. Rehman,Generalized derivation and commutativity of prime rings, Indian J. Pure Appl. Math.34(9) (2003), 1393-1396. · Zbl 1047.16020 |
| [17] | R. Raina, V. K. Bhat and N. Kumari,Commutativity of primeΓ-near-rings with(σ, τ)-derivation, Acta Math. Acad. Paedagog. Nyhazi25(2009), 165-173. · Zbl 1208.16037 |
| [18] | N. Ur-Rehman,On commutativity of rings with generalized derivations, Math. J. Okayama Univ. 44(2002), 43-49. · Zbl 1030.16022 |
| [19] | Y. Shang,A study of derivations in prime near-rings 1, Math. Balkanica (N.S.)25(4) (2011), 413-418. · Zbl 1269.16043 |
| [20] | X. K. Wang,Derivations in prime near-rings, Proc. Amer. Math. Soc.121(1994), 361-366. 1 · Zbl 0811.16040 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
