2000 character limit reached
On Jordan superderivations and Jordan super-biderivations of trivial extensions and triangular matrix rings
Published 20 Feb 2024 in math.RA | (2402.12611v1)
Abstract: Triangular matrix rings are example of trivial extensions. In this article we describe the Jordan superderivations of the trivial extensions and upper triangular matrix rings. We deduce then that any Jordan superderivation of an upper triangular matrix ring, under some conditions, is a derivation, and any Jordan super-biderivation of a trivial extension, and hence an upper triangular matrix ring, is a Jordan biderivation.
- I. Assem, D. Happel and O. Roldán, Representation-finite trivial extension algebras, Pure Appl. Algebra, 33 (1984) 235-242.
- K. I. Beidar, M. Brešar and M. A. Chebotar, Jordan superhomomorphism, Comm. Algebra, 31 (2003) 633-644.
- D. Benkovič, Jordan derivations and antiderivations on triangular matrices, Linear Algebra Appl. 397 (2005) 235-244.
- M. Brešar, Jordan derivation on semiprime rings, Proc. Amer. Math. Soc. 104 (1988) 1003-1006.
- M. Fošner, Jordan Superderivations, Comm. Algebra, 31 (2003) 4533-4545.
- M. Fošner, On the extended centroid of prime associative superalgebras with applications to superderivations, Comm. Algebra, 32 (2004) 689-705.
- H. Ghahramani, Jordan derivations on trivial extensions, Bull. Iranian Math. Soc. 39 (2013) 635-645.
- H. Ghahramani, M.N. Ghosseiri and S. Safari, Some questions concerning to superderivations on ℤ2−limit-fromsubscriptℤ2\mathbb{Z}_{2}-blackboard_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT -graded rings, Aequat. Math. 91 (2017) 725-738.
- M.N. Ghosseiri, Derivations and biderivations of trivial extensions and triangular matrix rings, Bull. Iranian Math. Soc. 43 (2017) 1629-1644.
- M.N. Ghosseiri, On Jordan left derivations and generalized Jordan left derivations of matrix rings, Bull. Iranian Math. Soc. 38(3) (2012) 689-698.
- D. A. Hadj Ahmed, On Jordan biderivations of triangular matrix rings, J. Math. Res. Appl. 36 (2016) 162-170.
- I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957) 1104-1110.
- Trivial extensions of tilted algebras, Proc. London Math. Soc. 46 (1993) 347-364.
- Y. Kitamura, On quotient rings of trivial extensions, Proc. Amer. Math. Soc. 88 (1983) 391-396.
- Additive Jordan derivations of reflexive algebras, J. Math. Anal. Appl. 329 (2007) 102-111.
- A.M. Sinclair, Jordan homomorphisms and derivations on semisimple Banach algebras, Proc. Amer. Math. Soc. 24 (1970) 209-214.
- Jordan derivations of triangular algebras, Linear Algebra Appl. 419 (2006) 251-255.
- J.-H. Zhang, Jordan derivations on nest algebras, Acta Math. Sinica, 41 (1998) 205-212.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.