پیوندهای مفید
آمار
| تعداد نشریات | 32 |
| تعداد شمارهها | 826 |
| تعداد مقالات | 7,979 |
| تعداد مشاهده مقاله | 42,420,208 |
| تعداد دریافت فایل اصل مقاله | 8,525,106 |
Commutativity of prime rings involving multiplicative b-generalized derivation | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 2، اسفند 2025، صفحه 165-176 اصل مقاله (153.9 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.26837.1635 | ||
| نویسندگان | ||
| W. Ahmed* 1؛ M. R. Mozumder1؛ A. Abbasi2؛ H. M. Alnoghashi3 | ||
| 1Department of Mathematics, Sreenidhi University, Hyderabad, India | ||
| 2School of Advanced Science and Languages, VIT Bhopal University, Madhya Pradesh, India | ||
| 3Department of Mathematics, Amran University, Amran, Yemen | ||
| چکیده | ||
| Let $\Qa_{mr}$ be a maximal right ring of quotients of $\Aa$, where $\Aa$ is a prime ring. A map $\Fa : \Aa \rightarrow \Qa_{mr}$ associated with derivation $d : \Aa \rightarrow \Aa$ is called a multiplicative $b$-generalized derivation (need not necessarily additive) if $\Fa(l m ) = \Fa(l )m + bl d(m )$ holds for all $l ,m \in \Aa$ and for some $b \in \Qa_{mr}$. In this article, we study the commutativity of prime rings when the map $b$-generalized derivation satisfies the strong commutativity preserving condition and some central identities. | ||
| کلیدواژهها | ||
| Derivation؛ Prime ring؛ Multiplicative generalized derivation؛ Multiplicative b-generalized derivation | ||
| مراجع | ||
|
[1] W. Ahmed and M. R. Mozumder, Study of multiplicative b-generalized derivation and its additivity, J. Algebra Relat. Topics, (1) 11 (2023), 111-123. [2] A. Ali, M. Yasen and M. Anwar, Strong commutativity preserving mappings on semi-prime rings, Bull. Korean Math. Soc., (4) 43 (2006), 711-713. [3] M. Ashraf, A. Ali and S. Ali, Some commutativity theorem for prime rings with generalized derivations, Southeast Asian Bull. Math., 31 (2007), 415-421. [4] K. I. Beidar, W. S. Martindale III and A. V. Mikhalev, Rings with generalized identities, Pure Appl. Math. Dekker, New York, (1996). [5] H. E. Bell and M. N. Daif, On commutativity and strong commutativity preserving maps, Canad. Math. Bull., (4) 37 (1994), 443-447. [6] M. Brešar, W. S. Martindale III and C. R. Miers, Centralizing maps in prime rings with involution, J. Algebra App., 161 (1993), 342-357. [7] V. De Filippis and F. Wei, b-generalized skew derivations on Lie ideals, Mediterr. J. Math., (2) 15 (2018), pp-24. [8] Ö. Gölbaşi, Multiplicative generalized derivations on ideals in semi-prime rings, Math. Slovaca, (6) 66 (2016), 1285-1296. [9] V. K. Kharchenko, Differential identity of prime rings, Algebra Logic, 17 (1978), 155-168. [10] E. Koç, Ö. Gölbaşi, Some results on ideals of semi-prime rings with multiplicative generalized derivations, Comm. Algebra, (11) 46 (2018), 4905-4913. [11] T. K. Lee and T. L. Wong, Nonadditive strong commutativity preserving maps, Commun. Algebra, 40 (2012), 2213–2218. [12] P. K. Liau and C. K. Liu, An Engel condition with b-generalized derivations for Lie ideals, J. Algebra App., (3) 17 (2018), 1850046, pp-17. [13] C. K. Liu, An Engel condition with b−generalized derivations, Linear Multilinear Algebra, (2) 65 (2017), 300-312. [14] J. Ma and X. W. Xu, Strong commutativity-preserving generalized derivations on semiprime rings, Acta Math. Sinica, (11) 24 (2008), 1835-1842. [15] J. H. Mayne, Centralizing mappings of prime rings, Canad. Math. Bull., 27 (1984), 122-126. [16] N. Rehman and M. S.Khan, A note on multiplicative (generalized)-skew derivation on semiprime rings, J. Taibah Univ. Sci., (4) 12 (2018), 450-454. | ||
|
آمار تعداد مشاهده مقاله: 126 تعداد دریافت فایل اصل مقاله: 19 |
||