Radicals of Skew Polynomial and Skew Laurent Polynomial Rings Over Skew Armendariz Rings

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].

Key Words:

• Armendariz ring
• Jacobson radical
• Prime radical
• Skew Laurent polynomial rings
• Skew polynomial rings

2010 AMS Subject Classification:

• 16S36
• 16N40
• 16N20

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.