135
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

On superderivations and super-biderivations of trivial extensions and triangular matrix rings

&
Pages 1662-1670 | Received 22 Apr 2018, Accepted 01 Aug 2018, Published online: 17 Dec 2018

References

  • Assem, I., Happel, D., Roldán, O. (1984). Representation-finite trivial extension algebras. Pure Appl. Algebra. 33:235–242.
  • Barker, G. P. (1989). Automorphisms groups of algebras of triangular matrices. Linear Algebra Appl. 121:207–215.
  • Benkovič, D. (2009). Biderivations of triangular algebras. Linear Algebra Appl. 431:1587–1602.
  • Brešar, M. (1994). On certain pairs of functions of semiprime rings. Proc. Am. Math. Soc. 120:709–713.
  • Brešar, M., Martindale III, W. S., Miers, C. R. (1993). Centralizing maps in prime rings with involusion. J. Algebra. 161:342–357.
  • Cheung, W.-S. (2000). Mappings on triangular algebras. PhD Dissertation. University of Victoria.
  • Coelho, S. P., Miles, C. P. (1993). Derivations of upper triangular matrix rings. Linear Algebra Appl. 187:263–267.
  • Eremita, D. (2017). Biderivations of triangular rings revisited. Bull. Malays. Math. Sci. Soc. 40(2):505–522.
  • Fošner, M. (2004). On the extended centroid of prime associative superalgebras with applications to superderivations. Commun. Algebra 32:689–705.
  • Ghahramani, H. (2013). Jordan derivations on trivial extensions. Bull. Iran. Math. Soc. 39:635–645.
  • Ghahramani, H., Ghosseiri, M. N., Safari, S. (2017). Some questions concerning to superderivations on Z2−graded rings. Aequat. Math. 91:725–738.
  • Ghosseiri, M. N. (2017). Derivations and biderivations of trivial extensions and triangular matrix rings. Bull. Iranian Math. Soc. 43:1629–1644.
  • Ghosseiri, M. N. (2013) On biderivations of upper triangular matrix rings. Linear Algebra Appl. 438:250–260.
  • Ghosseiri, M. N. (2005). The structure of (α, β)-derivations of triangular rings. Iran. J. Sci. Technol. Trans. A. 29(A3):507–514.
  • Hughes, D., Waschbusch, J. (1993). Trivial extensions of tilted algebras. Proc. Lond. Math. Soc. 46:347–364.
  • Jacobson, N. Abstract derivation and Lie algebras. Trans. Am. Math. Soc. 42(2):206–224.
  • Jøndrup, S. (1995). Automorphisms and derivations of triangular matrices. Linear Algebra Appl. 22:205–215.
  • Kitamura, Y. (1983). On quotient rings of trivial extensions. Proc. Am. Math. Soc. 88:391–396.
  • Kolesnikov, S. G., Mal’tsev, N. V. (2011). Derivations of a matrix ring containing a subring of triangular matrices, Russian Math. 55(11):23–33.
  • Maksa, G. (1980). A remark on symmetric biadditive functions having nonnegative diagonalization. Glasnik Math. 15(35):279–282.
  • Nagata, M. (1962). Local Rings. New York: Interscience Publishers.
  • Vukman, J. (1989). Symmetric bi-derivations on prime and semi-prime rings. Aequat. Math. 38:245–254.
  • Wang, Y. (2016). Biderivations of triangular rings. Linear Multilinear Algebra 64(10):1952–1959.
  • Zhao, Y., Wang, D., Yao, R. (2009). Biderivations of upper triangular matrix algebras over commutative rings. Int. J. Math. Game Theory Algebra 18:473–478.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.