Abstract
The self-idealization of a commutative ring R is isomorphic to the ring R[x]/(x(2)) or, equivalently, the ring of upper-triangular Toeplitz matrices T (R) = {((a b)(0 a)) : a, b is an element of R}. Recently, Chang and Smertnig characterized the sets of lengths of factorizations in T (D) where D is a principal ideal domain. In this work, in addition to correcting an error in their paper, we extend the study to T (R) when R is either a principal ideal ring or a unique factorization ring.