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   a note on derivations in rings and banach algebras  
   
نویسنده rehman nadeem ur ,huang shuliang ,raza mohd arif
منبع journal of algebraic structures and their applications - 2019 - دوره : 6 - شماره : 1 - صفحه:115 -125
چکیده    let $r$ be a prime ring with $u$ the utumi quotient ring and $q$ be the martindale quotient ring of $r$, respectively. let $d$ be a derivation of $r$ and $m,n$ be fixed positive integers. in this paper, we study the case when one of the following holds:$(i)$~ $d(x)circ_n d(y)$=$xcirc _m y$ $(ii)$~$d(x)circ_m d(y)$=$(d(xcirc y))^n$ for all $x,y$ in some appropriate subset of $r$. we also examine the case where $r$ is a semiprime ring. finally, as an application we apply our result to the continuous derivations on banach algebras.
کلیدواژه prime and semiprime rings ,derivations ,martindale ring of quotients ,banach algebras ,radical
آدرس aligarh muslim university, department of mathematics, india, chuzhou university, school of mathematics and finance, china, king abdulaziz university, faculty of science and arts-rabigh, department of mathematics, saudi arabia
پست الکترونیکی arifraza03@gmail.com
 
 

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