Article
| Title: | Jordan triple ($\theta ,\varphi $)-derivations of prime rings (English) |
| Author: | Kao, Tzu-Ying |
| Author: | Liu, Cheng-Kai |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 4 |
| Year: | 2025 |
| Pages: | 1229-1239 |
| Summary lang: | English |
| . | |
| Category: | math |
| . | |
| Summary: | Let $R$ be a 2-torsion free prime ring and let $\theta ,\varphi $ be endomorphisms of $R$. We prove that if $R$ is commutative, then every Jordan triple $(\theta ,\varphi )$-derivation of $R$ is a \hbox {$(\theta ,\varphi )$-derivation} and if $R$ is noncommutative, then every Jordan triple $(\theta ,\varphi )$-derivation of $R$ with either $\theta $ or $\varphi $ an epimorphism, is a $(\theta ,\varphi )$-derivation. As an application, we characterize Jordan triple semiderivations of prime rings. Our theorems naturally generalize the result for Jordan $(\theta ,\varphi )$-derivations obtained by M. Brešar, J. Vukman (1991) and the result for Jordan semiderivations obtained by V. De Filippis, A. Mamouni, L. Oukhtite (2015). (English) |
| Keyword: | $(\theta ,\varphi )$-derivation |
| Keyword: | Jordan $(\theta ,\varphi )$-derivation |
| Keyword: | Jordan triple $(\theta ,\varphi )$-derivation |
| MSC: | 16N60 |
| MSC: | 16W10 |
| MSC: | 16W25 |
| DOI: | 10.21136/CMJ.2025.0027-25 |
| . | |
| Date available: | 2025-12-20T07:19:55Z |
| Last updated: | 2025-12-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153239 |
| . | |
| Reference: | [1] Ali, S., Fošner, A., Fošner, M., Khan, M. S.: On generalized Jordan triple $(\alpha,\beta)^*$-derivations and related mappings.Mediterr. J. Math. 10 (2013), 1657-1668. Zbl 1285.16035, MR 3119325, 10.1007/s00009-013-0277-x |
| Reference: | [2] Ashraf, M., Ali, A., Ali, S.: On Lie ideals and generalized $(\theta,\phi)$-derivations on prime rings.Commun. Algebra 32 (2004), 2977-2985. Zbl 1068.16046, MR 2102162, 10.1081/AGB-120039276 |
| Reference: | [3] Ashraf, M., Siddeeque, M. A., Shikeh, A. H.: On the characterization of certain additive maps in prime $*$-rings.Czech. Math. J. 74 (2024), 549-565. Zbl 07893398, MR 4764539, 10.21136/CMJ.2024.0460-23 |
| Reference: | [4] Bell, H. E., III, W. S. Martindale: Semiderivations and commutativity in prime rings.Can. Math. Bull. 31 (1988), 500-508. Zbl 0627.16027, MR 0971579, 10.4153/CMB-1988-072-9 |
| Reference: | [5] Bergen, J.: Derivations in prime rings.Can. Math. Bull. 26 (1983), 267-270. Zbl 0525.16021, MR 0703394, 10.4153/CMB-1983-042-2 |
| Reference: | [6] Brešar, M.: Jordan derivations on semiprime rings.Proc. Am. Math. Soc. 104 (1988), 1003-1006. Zbl 0691.16039, MR 0929422, 10.1090/S0002-9939-1988-0929422-1 |
| Reference: | [7] Brešar, M.: Jordan mappings of semiprime rings.J. Algebra 127 (1989), 218-228. Zbl 0691.16040, MR 1029414, 10.1016/0021-8693(89)90285-8 |
| Reference: | [8] Brešar, M.: Semiderivations of prime rings.Proc. Am. Math. Soc. 108 (1990), 859-860. Zbl 0688.16038, MR 1007488, 10.1090/S0002-9939-1990-1007488-X |
| Reference: | [9] Brešar, M., Vukman, J.: Jordan derivations on prime rings.Bull. Aust. Math. Soc. 37 (1988), 321-322. Zbl 0634.16021, MR 0943433, 10.1017/S0004972700026927 |
| Reference: | [10] Brešar, M., Vukman, J.: Jordan $(\theta,\varphi)$-derivations.Glas. Math., III. Ser. 26 (1991), 13-17. Zbl 0798.16023, MR 1269170 |
| Reference: | [11] Chang, C.-W., Liu, C.-K.: Derivations characterized by monomials $x^{2n}$ in prime rings.J. Algebra Appl. 23 (2024), Article ID 2450237, 31 pages. Zbl 07960555, MR 4833980, 10.1142/S0219498824502372 |
| Reference: | [12] Filippis, V. De, Mamouni, A., Oukhtite, L.: Generalized Jordan semiderivations in prime rings.Can. Math. Bull. 58 (2015), 263-270. Zbl 1326.16037, MR 3334920, 10.4153/CMB-2014-066-9 |
| Reference: | [13] B. L. M. Ferreira, R. N. Ferreira, H. Guzzo, Jr.: Generalized Jordan derivations on semiprime rings.J. Aust. Math. Soc. 109 (2020), 36-43. Zbl 1448.16044, MR 4120795, 10.1017/S1446788719000259 |
| Reference: | [14] Fošner, A., Vukman, J.: On certain functional equations related to Jordan triple $(\theta,\phi)$-derivations on semiprime rings.Monatsh. Math. 162 (2011), 157-165. Zbl 1216.16034, MR 2769884, 10.1007/s00605-009-0154-7 |
| Reference: | [15] Gölbaşı, Ã ., Koç, E.: Notes on Jordan $(\sigma,\tau)^*$-derivations and Jordan triple $(\sigma,\tau)^*$-derivations.Aequationes Math. 85 (2013), 581-591. Zbl 1271.16044, MR 3063891, 10.1007/s00010-012-0149-7 |
| Reference: | [16] Herstein, I. N.: Jordan derivations of prime rings.Proc. Am. Math. Soc. 8 (1957), 1104-1110. Zbl 0216.07202, MR 0095864, 10.1090/S0002-9939-1957-0095864-2 |
| Reference: | [17] Jing, W., Lu, S.: Generalized Jordan derivations on prime rings and standard operator algebras.Taiwanese J. Math. 7 (2003), 605-613. Zbl 1058.16031, MR 2017914, 10.11650/twjm/1500407580 |
| Reference: | [18] Lee, T.-K.: Functional identities and Jordan $\sigma$-derivations.Linear Multilinear Algebra 64 (2016), 221-234. Zbl 1346.16016, MR 3434517, 10.1080/03081087.2015.1032200 |
| Reference: | [19] Lee, T.-K.: Jordan $\sigma$-derivations of prime rings.Rocky Mt. J. Math. 47 (2017), 511-525. Zbl 1371.16020, MR 3635372, 10.1216/RMJ-2017-47-2-511 |
| Reference: | [20] Leroy, A., Matczuk, J.: Quelques remarques à propos des $S$-dérivations.Commun. Algebra 13 (1985), 1229-1244 French. Zbl 0569.16028, MR 0788760, 10.1080/00927878508823216 |
| Reference: | [21] Liu, C.-K.: Generalized derivations with nilpotent values in semiprime rings.Quaest. Math. 47 (2024), 1195-1212. Zbl 07880826, MR 4760436, 10.2989/16073606.2023.2283137 |
| Reference: | [22] Liu, C.-K., Shiue, W.-K.: Generalized Jordan triple $(\theta,\phi)$-derivations on semiprime rings.Taiwanese J. Math. 11 (2007), 1397-1406. Zbl 1143.16036, MR 2368657, 10.11650/twjm/1500404872 |
| Reference: | [23] Siddeeque, M. A., Khan, N., Abdullah, A. A.: Weak Jordan $*$-derivations of prime rings.J. Algebra Appl. 22 (2023), Article ID 2350105, 34 pages. Zbl 1541.16036, MR 4556321, 10.1142/S0219498823501050 |
| Reference: | [24] Vukman, J.: A note on generalized derivations of semiprime rings.Taiwanese J. Math. 11 (2007), 367-370. Zbl 1124.16030, MR 2333351, 10.11650/twjm/1500404694 |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
