Note on Sus̆kevic̆’s problem on zero divisors

ABSTRACT

We solve an old Sus̆kevic̆’s problem on right zero divisors in the ring T(∞,K) of infinite ℕ×ℕ upper triangular matrices over a field K. In the solution we use a notion of strong linear independence.

KEYWORDS:

• Upper triangular infinite matrix
• zero divisor in matrix ring

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16U99
• 16S50
• 15A03

Acknowledgement

We thank Prof. V. Sushchanskyy for bringing to our attention the paper [4] and useful comments.