Abstract
In this note we study radicals of skew polynomial ring R[x; α] and skew Laurent polynomial ring R[x, x −1; α], for a skew-Armendariz ring R. In particular, among the other results, we show that for an skew-Armendariz ring R, J(R[x; α]) = N 0(R[x; α]) = Niℓ*(R)[x; α] and J(R[x, x −1; α]) = N 0(R[x, x −1; α]) = Niℓ*(R)[x, x −1; α].
ACKNOWLEDGMENT
The author would like to thank the Banach Algebra Center of Excellence for Mathematics, University of Isfahan. Special thanks are due to the referee who read this article very carefully and made many useful suggestions.
This research was in part supported by a grant from IPM (No. 89160029).
Notes
Communicated by V. A. Artamonov.