On a Quotient of Polynomial Rings

Abstract

For a ring R we study an ideal theory of a triangular matrix ring and use it to determine radicals and prime ideals of the ring R[x]/⟨x ⁿ ⟩, for each positive integer n, where R[x] is the ring of polynomials in an indeterminant x, and ⟨x ⁿ ⟩ is the ideal generated by x ⁿ .

Key Words:

• Jacobson radical
• Polynomial rings
• Triangular matrix rings

2000 Mathematics Subject Classification:

• 16S36, 16N40

Notes

Communicated by V. A. Artamonov.