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Let $\mathfrak{R}$ be a commutative ring with unity, $\mathrm{A}$ and $\mathrm{B}$ be $\mathfrak{R}$-algebras, $\mathrm{M}$ be a $(\mathrm{A}, \mathrm{B})$-bimodule and $\mathrm{N}$ be a $(\mathrm{B}, \mathrm{A})$-bimodule. The $\mathfrak{R}$-algebra $\mathfrak{S}=\mathfrak{S}(\mathrm{A}, \mathrm{M}, \mathrm{N}, \mathrm{B})$ 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 generalized derivation and generalized Jordan derivation on generalized matrix algebras and prove that every generalized Jordan derivation can be written as the sum of a generalized derivation and antiderivation with some limitations. Also, we show that every generalized Jordan derivation is a generalized derivation on trivial generalized matrix algebra over a field.
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참고문헌 (16)
참고문헌 신청
M. Ashraf / 2017 / Nonlinear generalized Lie triple derivation on triangular algebras / Comm. Algebra 45(10):4380~4395
M. Breˇsar / 1989 / Jordan mappings of semiprime rings / J. Algebra 127(1):218~228
M. Breˇsar / 1991 / On the distance of the composition of two derivations to the generalized derivations / Glasgow Math. J 33(1):89~93
W. S. Cheung / 2000 / Mappings on triangular algebras
I. N. Herstein / 1957 / Jordan derivations of prime rings / Proc. Amer. Math. Soc 8:1104~1110
M. Breˇsar / 1989 / Jordan mappings of semiprime rings / J. Algebra 127(1):218~228
M. Breˇsar / 1991 / On the distance of the composition of two derivations to the generalized derivations / Glasgow Math. J 33(1):89~93
W. S. Cheung / 2000 / Mappings on triangular algebras
I. N. Herstein / 1957 / Jordan derivations of prime rings / Proc. Amer. Math. Soc 8:1104~1110
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