Jordan generalized derivations on trivial extension algebras
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In this paper, we investigate the problem of describing the form of Jordan generalized derivations on trivial extension algebras. One of the main results shows, under some conditions, that every Jordan generalized derivation on a trivial extension algebra is the sum of a generalized derivation and an antiderivation. This result extends the study of Jordan generalized derivations on triangular algebras (see [12]), and also it can be considered as a ``generalized" counterpart of the results given on Jordan derivations of a trivial extension algebra (see [11]).
Abstract
In this paper, we investigate the problem of describing the form of Jordan generalized derivations on trivial extension algebras. One of the main results shows, under some conditions, that every Jordan generalized derivation on a trivial extension algebra is the sum of a generalized derivation and an antiderivation. This result extends the study of Jordan generalized derivations on triangular algebras (see [12]), and also it can be considered as a ``generalized" counterpart of the results given on Jordan derivations of a trivial extension algebra (see [11]).
참고문헌 (17)
- K. I. Beidar, "On additive isomorphisms of prime rings preserving polynomials", J. Algebra, 217, pp.650~667 (1999)[DOI]
- D. Benkovic, "A note on f-derivations of triangular algebras", Aequationes Math., 89(4), pp.1207~1211 (2015)[DOI]
- D. Benkovic, "Lie triple derivations of unital algebras with idempotents", Linear Multilinear Algebra, 63(1), pp.141~165 (2015)[DOI]
- D. Benkovic, "Commuting traces and commutativity preserving maps on triangular algebras", J. Algebra, 280(2), pp.797~824 (2004)[DOI]
- D. Bennis, "Derivations and the first cohomology group of trivial extension algebras", Mediterr. J. Math., 14(4), pp.18~ (2017)[DOI]
- G. F. Birkenmeier, "Extensions of Rings and Modules", pp.2013, Birkhauser
- W.-S. Cheung, "Mappings on triangular algebras" (2000), ProQuest LLC
- W.-S. Cheung, "Lie derivations of triangular algebras", Linear Multilinear Algebra, 51(3), pp.299~310 (2003)[DOI]
- Hamid Reza Ebrahimi Vishki, "Jordan higher derivations on trivial extension algebras", 대한수학회논문집, 31(2), pp.247~259 (2016), 대한수학회
- M. Fosner, "On Jordan triple derivations and related mappings", Mediterr. J. Math., 5(4), pp.415~427 (2008)[DOI]
- H. Ghahramani, "Jordan derivations on trivial extensions", Bull. Iranian Math. Soc., 39(4), pp.635~645 (2013)
- Y. Li, "Jordan generalized derivations on triangular algebras", Linear Multilinear Algebra, 59(8), pp.841~849 (2011)[DOI]
- H. Li, "Generalized Lie triple derivations", Linear Multilinear Algebra, 59(3), pp.237~247 (2011)[DOI]
- A. H. Mokhtari, "Lie derivations on trivial extension algebras", Ann. Math. Sil., 31(1), pp.141~153 (2017)
- A. Nakajima, "On generalized higher derivations", Turkish J. Math., 24(3), pp.295~311 (2000)
- J. Wu, "Generalized Jordan derivations on prime rings and standard operator algebras", Taiwanese J. Math., 7(4), pp.605~613 (2003)[DOI]
- Y. Zhang, "Weak amenability of module extensions of Banach algebras", Trans. Amer. Math. Soc., 354(10), pp.4131~4151 (2002)[DOI]