The semigroup of non left zero divisors in an algebra, infinite powers of matrices and related matters (Q1057967)

The author is concerned with rings having one-sided zerodivisors, e.g. the set of all \(n\times n\) matrices over a field with zero last row. She also reports on a paper (not quoted) in which complex matrices C satisfying \(C^ n\to 0\) are characterized by the existence of a positive-definite matrix H such that \(H-CHC^*>0\); this is related to Lyapunov's theorem on stable matrices.