On Skew Triangular Matrix Rings

Abstract

For a ring R, endomorphism α of R and positive integer n we define a skew triangular matrix ring T _n (R, α). By using an ideal theory of a skew triangular matrix ring T _n (R, α) we can determine prime, primitive, maximal ideals and radicals of the ring R[x; α]/ ⟨ x ⁿ  ⟩, for each positive integer n, where R[x; α] is the skew polynomial ring, and ⟨ x ⁿ  ⟩ is the ideal generated by x ⁿ .

Key Words:

• Jacobson radical
• Prime ideals
• Skew polynomial rings

2000 Mathematics Subject Classification:

• 16S36
• 16N20

ACKNOWLEDGMENT

This research was partially supported by the Center of Excellence for Mathematics, University of Isfahan.

Notes

Communicated by V. A. Artamonov.