Ideals and symmetric reverse bi-derivations of prime and semiprime rings

C. Jaya Subba Reddy1* A. Siva Kameswara Kumar2 and B. Ramoorthy Reddy3

doi:10.26637/MJM0601/0033

Ideals and symmetric reverse bi-derivations of prime and semiprime rings

Authors :

C. Jaya Subba Reddy^1* A. Siva Kameswara Kumar² and B. Ramoorthy Reddy³

Author Address :

^1,3Department of Mathematics, Sri Venkateswara University, Tirupati-517502, Andhra Pradesh, India.
²Research Scholar, Department of Mathematics, Rayalaseema University, Kurnool-518002, Andhra Pradesh, India.

*Corresponding author

Abstract :

Let $R$ be a prime ring of char $R e 2$ and $I$ a nonzero ideal of $R$. Suppose that there exist symmetric reverse bi-derivations $D_{1}(.,.):RXR ightarrow R$ and $D_{2} (.,.):RXR ightarrow R$ such that $D_{1} (d_{2}(x),x)=0$ for all $xin I$, where $d_{2}$ denotes the trace of $D_{2}$. Then either $D_{1}=0$ or $D_{2}=0$.

Keywords :

Derivation, Reverse derivation, Symmetric bi-derivation, Symmetric reverse bi-derivation, Prime rings, Semiprime rings, Trace.

DOI :

10.26637/MJM0601/0033

Article Info :

Received : October 11, 2017; Accepted : December 27, 2017.