Radicals of matrix rings generated by a companion matrix

ABSTRACT

The radicals of full matrix rings as well as structural matrix rings have been studied extensively and there is a well-developed theory for both. Here we initiate the radical theory for another class of matrix rings over a given ring; the matrix ring generated by the companion matrix of a polynomial over the ring.

KEYWORDS:

• Barnett matrix ring
• companion matrix
• Jacobson radical
• nil radical

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16N80
• 16N20
• 16N40
• 16S50
• 15B99