Abstract
The aim of this note is to study properties of the generalized centroid of the semi-prime gamma rings. Main results are the following theorems: (1) Let M be a semi-prime <TEX>$\Gamma$</TEX>-ring and Q a quotient <TEX>$\Gamma$</TEX>-ring of M. If W is a non-zero submodule of the right (left) M-module Q, then <TEX>$W\Gamma$W</TEX> <TEX>$\neq</TEX> 0. Furthermore Q is a semi-prime <TEX>$\Gamma$</TEX>-ring. (2) Let M be a semi-prime <TEX>$\Gamma$</TEX>-ring and <TEX>$C_{{Gamma}$</TEX> the generalized centroid of M. Then <TEX>$C_{\Gamma}$</TEX> is a regular <TEX>$\Gamma$</TEX>-ring. (3) Let M be a semi-prime <TEX>$\Gamma$</TEX>-ring and <TEX>$C_{\gamma}$</TEX> the extended centroid of M. If <TEX>$C_{\gamma}$</TEX> is a <TEX>$\Gamma$</TEX>-field, then the <TEX>$\Gamma$</TEX>-ring M is a prime <TEX>$\Gamma$</TEX>-ring.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
