TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Generalized (a, b)-reverse derivations in semi prime near rings

, , * , ,

* Corresponding author · click or hover a name for details

pp. 1639–1664Vol. 26Issue 6September 2023DOI: 10.47974/JDMSC-1571 Crossmark XML
Received:
07 Jul 2021
Accepted:
06 Jan 2022
Published Online:
30 Sep 2023
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1571
Pages:
1639–1664

Abstract

In this paper, our aim is to study the right generalized (a, b)-reverse derivations on semi-prime near-ring and generalized dependent element of right generalized (a, b)-reverse derivation and right generalized b-reverse derivation on semi-prime near-ring. We generalize some useful results by using these notions. 

Keywords

Subject Classifications

(2010) 16Y3016N6016W2016W25

References

[1] Howard E Bell and Gordon Mason, On derivations in near-rings, North-Holland Mathematics Studies, vol. 137, Elsevier, 1987, pp. 31–35.
[2] Abdelkarim Boua, Some identities in rings and near-rings with derivations, Kragujevac Journal of Mathematics 45 (2012), no. 1, 75–80.
[3] Matej BreŠar, One-sided ideals and derivations of prime rings, Proceedings of the American Mathematical Society (1994), 979–983.
[4] Matej BreŠar and Joso Vukman, On some additive mappings in rings with involution, aequationes mathematicae 38 (1989), no. 2-3, 178–185.
[5] Chen-Lian Chuang, Tsiu-Kwen Lee, Cheng-Kai Liu, and Yuan-Tsung Tsai, Higher derivations of ore extensions, Israel Journal of Mathematics 175 (2010), no. 1, 157–178.
[6] Mohamad Nagy Daif and Howard E Bell, Remarks on derivations on semiprime rings, International Journal of Mathematics and Mathematical Sciences 15 (1992).
[7] Basudeb Dhara, Remarks on generalized derivations in prime and semiprime rings, International Journal of Mathematics and Mathematical Sciences 2010 (2010).
[8] Öznur GÖlbaşi and KOC. Emine, Notes on commutativity of prime rings with generalized derivation, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 58 (2009), no. 2, 39–46.
[9] IN Herstein, Jordan derivations of prime rings, Proceedings of the American Mathematical Society 8 (1957), no. 6, 1104–1110.
[10] L Madhuchelvi and B Nivetha, Generalized reverse derivations in semiprime near-rings, The International Journal of Analytical and Experimental Modal Analysis 12 (2020).
[11] MA Quadri, M Shadab Khan, and N Rehman, Generalized derivations and commutativity of prime rings, Indian Journal of Pure and Applied Mathematics 34 (2003), no. 9, 1393–1396.
[12] Mohammad Samman and Nouf Alyamani, Derivations and reverse derivations in semiprime rings, International Mathematical Forum, vol. 2, 2007, pp. 1895–1902.
[13] RK Sharma and B Prajapati, Lie ideal and generalized jordan left derivation on semiprime rings, Italian J. of Pure and Applied Math (2013), 15–22.
[14] Monrudee Sirivoravit and Utsanee Leerawat, On a generalization of reverse derivation of certain algebraic structure, Journal of Discrete Mathematical Sciences and Cryptography 23 (2020), no. 5, 1069–1076.
[15] AB Thaheem, On some properties of derivations on semiprime rings., Southeast Asian Bulletin of Mathematics 29 (2005), no. 6.
[16] Nadeem Ur-Rehman, On commutativity of rings with generalized derivations, Math. J Okayama Univ 44 (2002), 43–49.
[17] Tasiu Abdullahi Yusuf, Commutativity results on prime near-rings involving reverse derivation, Mohammed First University Faculty of Sciences Department of Mathematics (2019), 126.

Views: 205Downloads: 75Citations: 0