On multiplicative (generalized) - derivations and central valued conditions in prime rings

• Autorzy: Sandhu Gurninder S. , Ayran Ayşe , Aydin Neşet

Identyfikatory

DOI

10.7862/rf.2021.7

• Języki publikacji: EN

Abstrakty

EN

Let R be a prime ring with multiplicative (generalized)- derivations (F, f) and (G, g) on R. This paper gives a number of central valued algebraic identities involving F and G that are equivalent to the commutativity of R under some suitable assumptions. Moreover, in order to optimize our results, we show that the assumptions taken cannot be relaxed.

Słowa kluczowe

EN

prime ring; multiplicative generalized derivation; one-sided ideal; commutativity

PL

teoria pierścieni; ideał jednostronny; przemienność

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2021
• Tom: Vol. 44
• Strony: 93--105
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Sandhu Gurninder S.

• Department of Mathematics, Patel Memorial National College, Rajpura-140401, Punjab, India

• https://orcid.org/0000-0001-8618-6325

autor

Ayran Ayşe

• Department of Mathematics, Çanakkale Onsekiz Mart University, Çanakkale-17020, Turkey

• https://orcid.org/+0000-0002-1626-5498

autor

Aydin Neşet

• Department of Mathematics, Çanakkale Onsekiz Mart University, Çanakkale-17020, Turkey

• https://orcid.org/0000-0002-7193-3399

Bibliografia

• [1] E. Albaş, On generalized derivations satisfying certain identities, Ukrain. Math. J. 63 (1) (2011) 596-602. DOI: 10.1007 /s11253-011-0535-7.
• [2] A. Ali, B. Dhara, S. Khan, F. Ali, Multiplicative (generalized)-derivations and left ideals in semiprime rings, Hacettepe J. Math. Stat. 44 (6) (2015) 1293-1306.
• [3] M. Ashraf, N. Rehman, On derivations and commutativity in prime rings, East-West J. Math. 3 (1) (2001) 87-91.
• [4] M. Ashraf, A. Ali, S. Ali, Some commutativity theorems for rings with generalized derivations, Southeast Asian Bull. Math. 31 (2007) 415-421.
• [5] H.E. Bell, W.S. Martindale III, Centralizing mappings of semiprime rings, Canad. Math. Bull. 30 (1) (1987) 92-101. DOI: 10.4153 /CMB-1987-014-x.
• [6] D.K. Camci, N. Aydin, On multiplicative (generalized)-derivations in semiprime rings, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 66 (1) (2017) 153-164. DOI:10.1501/Commua10000000784.
• [7] B. Dhara, S. Ali, On multiplicative (generalized)-derivations in prime and semiprime rings, Aequat. Math. 86 (2013) 65-79. DOI: 10.1007/s00010-013-0205-y.
• [8] B. Dhara, K.G. Pradhan, A note on multiplicative (generalized)-derivations with annihilator conditions, Georgian Math. J. 23 (2) (2016) 191-198. DOI:10.1515/gmj-2016-0020.
• [9] I. Gusić, A note on generalized derivations of prime rings, Glasnik Mate. 40 (60) (2005) 47-49.
• [10] S. Huang, Generalized reverse derivations and commutativity of prime rings, Commun. Math. 27 (2019) 43-50. DOI:10.2478/cm-2019-0004.
• [11] E.C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957) 1093-1100. DOI: 10.2307/2032686.
• [12] N. Rehman, R.M. Al-Omary, N.M. Muthana, A note on multiplicative (generalized) (α, β)-derivations in prime rings, Annales Math. Silesianae 33 (2019) 266-275.
• [13] G.S. Sandhu, D. Kumar, A note on derivations and Jordan ideals of prime rings, AIMS Math. 2 (4) (2017) 580-585. DOI:10.3934/Math.2017.4.580; correction 4 (3) (2019) 684-685. DOI:10.3934/Math.2019.3.684.
• [14] G.S. Sandhu, D. Kumar, Derivations satisfying certain algebraic identities on Lie ideals, Math. Morav. 23 (2) (2019) 79-86. DOI:10.5937/MatMor1902079S.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).