مشخصات پژوهش

عنوان	ON JORDAN LEFT DERIVATIONS AND GENERALIZED JORDAN LEFT DERIVATIONS OF MATRIX RINGS
نوع پژوهش	مقاله چاپ‌شده در مجلات علمی
کلیدواژه‌ها	Prime ring, left derivation, Jordan left derivation, generalized left derivation, generalized Jordan left derivation.
چکیده	Let $R$ be a $2$-torsion free ring with identity. In this paper, fi rst we prove that any Jordan left derivation (hence, any left derivation) on the full matrix ring $M_n(R) (n\geq  2)$ is identically zero, and any generalized left derivation on this ring is a right centralizer. Next, we show that if R is also a prime ring and $n\geq  1$, then any Jordan left derivation on the ring $T_n(R)$ of all nn upper triangular matrices over $R$ is a left derivation, and any generalized Jordan left derivation on $T_n(R)$ is a generalized left derivation. Moreover, we prove that any generalized left derivation on $T_n(R)$ is decomposed into the sum of a right centralizer and a Jordan left derivation. Some related results are also obtained.
پژوهشگران	محمد نادر قصیری (نفر اول)