Elliott and Kucerovsky stated that a nonunital extension of separable
-algebras
with a stable ideal is nuclearly absorbing if and only if the extension is
purely large. However, their proof was flawed. We give a counterexample to
their theorem as stated, but establish an equivalent formulation of nuclear
absorption under a very mild additional assumption to being purely large. In
particular, if the quotient algebra is nonunital, then we show that the original
theorem applies. We also examine how this affects results in classification
theory.
