Riv. Mat. Univ. Parma, Vol. 12, No. 2, 2021
Mohammad Ashraf [a] and Aisha Jabeen [b]
On generalized matrix algebras having multiplicative generalized Lie type derivations
Pages: 267-285
Received: 29 October 2020
Accepted in revised form: 20 April 2021
Mathematics Subject Classification: 16W25, 47L35, 15A78.
Keywords: Generalized matrix algebras, generalized derivation, generalized Lie derivation.
Authors address:
[a]: Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India.
[b]: Department of Applied Sciences & Humanities, Jamia Millia Islamia, New Delhi-110025, India.
Full Text (PDF)
The first author is partially supported by MATRICS research grant from DST(SERB) (MTR/2017/000033).
Also, this work has been sponsored by Dr. D. S. Kothari Postdoctoral Fellowship
(Award letter No. F.4-2/2006(BSR)/MA/18-19/0014) awarded to the second author
under the University Grants Commission, Government of India, New Delhi.
Abstract:
Let \(\mathfrak{R}\) be a commutative ring with unity. The \(\mathfrak{R}\)-algebra \(\mathfrak{G}=\mathfrak{G}(\mathrm{A}, \mathrm{M}, \mathrm{N}, \mathrm{B})\)
is a generalized matrix algebra defined by the Morita context \((\mathrm{A}, \mathrm{B}, \mathrm{M}, \mathrm{N}, \xi_{\mathrm{M}\mathrm{N}}, \Omega_{\mathrm{N}\mathrm{M}}).\)
In this article, we study multiplicative generalized Lie type derivations on generalized matrix algebras and prove that it has the standard form.
References
- [1]
-
I. Z. Abdullaev, \(n\)-Lie derivations on von Neumann algebra,
Uzbek. Mat. Zh. 5 (1992), 3-9.
MR1258290
- [2]
-
M. Ashraf and A. Jabeen,
Nonlinear generalized Lie triple derivations on triangular algebras,
Comm. Algebra 45 (2017), 4380-4395.
MR3640815
- [3]
-
M. Ashraf and A. Jabeen,
On generalized Jordan derivations of generalized matrix algebras,
Commun. Korean Math. Soc. 35 (2020), 733-744.
MR4160721
- [4]
-
L. Chen and J. Zhang,
Nonlinear Lie derivations on upper triangular matrices,
Linear Multilinear Algebra 56 (2008), 725-730.
MR2457697
- [5]
-
W. S. Cheung,
Mappings on triangular algebras,
Ph.D. dissertation, University of Victoria, 2000.
Handle
- [6]
-
Y. Du and Y. Wang,
Lie derivations of generalized matrix algebras,
Linear Algebra Appl. 437 (2012), 2719-2726.
MR2964719
- [7]
-
A. Jabeen,
Multiplicative generalized Lie triple derivations on generalized matrix algebras,
Quaest. Math. 44 (2021), 243-257.
MR4225654
- [8]
-
P. Ji, R. Liu and Y. Zhao,
Nonlinear Lie triple derivations of triangular algebras,
Linear Multilinear Algebra 60 (2012), 1155-1164.
MR2983757
- [9]
-
P. S. Ji and L. Wang,
Lie triple derivations on TUHF algebras,
Linear Algebra Appl. 403 (2005), 399-408.
MR2140293
- [10]
-
Y. B. Li and F. Wei,
Semi-centralizing maps of generalized matrix algebras,
Linear Algebra Appl. 436 (2012), 1122-1153.
MR2890909
- [11]
-
Y. B. Li, L. van Wyk and F. Wei,
Jordan derivations and antiderivations of generalized matrix algebras,
Oper. Matrices 7 (2013), 399-415.
MR3099192
- [12]
-
Y. B. Li and Z. K. Xiao,
Additivity of maps on generalized matrix algebras,
Electron. J. Linear Algebra 22 (2011), 743-757.
MR2831027
- [13]
-
X. F. Liang, F. Wei, Z. K. Xiao and A. Fošner,
Centralizing traces and Lie triple isomorphisms on generalized matrix algebras,
Linear Multilinear Algebra 63 (2015), 1786-1816.
MR3305010
- [14]
-
W. Lin,
Nonlinear generalized Lie \(n\)-derivations on triangular algebras,
Comm. Algebra 46 (2018), 2368-2383.
MR3778397
- [15]
-
F. Y. Lu and W. Jing,
Characterizations of Lie derivations of \({B(X)}\),
Linear Algebra Appl. 432 (2010), 89-99.
MR2566460
- [16]
-
W. S. Martindale,
Lie derivations of primitive rings,
Michigan Math. J. 11 (1964), 183-187.
MR0166234
- [17]
-
A. H. Mokhtari and H. R. E. Vishki,
More on Lie derivations of a generalized matrix algebra,
Miskolc Math. Notes 19 (2018), 385-396.
MR3895592
- [18]
-
K. Morita,
Duality for modules and its applications to the theory of rings with minimum condition,
Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 6 (1958), 83-142.
MR0096700
- [19]
-
X. Qi,
Characterizing Lie \(n\)-derivations for reflexive algebras,
Linear Multilinear Algebra 63 (2015), 1693-1706.
MR3305003
- [20]
-
A. D. Sands,
Radicals and Morita contexts,
J. Algebra 24 (1973), 335-345.
MR0327815
- [21]
-
Y. Wang,
Lie \(n\)-derivations of unital algebras with idempotents,
Linear Algebra Appl. 458 (2014), 512-525.
MR3231830
- [22]
-
Y. Wang and Y. Wang,
Multiplicative Lie \(n\)-derivations of generalized matrix algebras,
Linear Algebra Appl. 438 (2013), 2599-2616.
MR3005317
- [23]
-
Z. K. Xiao and F. Wei,
Commuting mappings of generalized matrix algebras,
Linear Algebra Appl. 433 (2010), 2178-2197.
MR2736145
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