  Let R be a commutative noetherian ring. Lindo and Pande have recently posed
the question asking when every ideal of R is isomorphic to some trace ideal of
R. This paper studies this question and gives several answers. In particular, a
complete answer is given in the case where R is local: it is proved in this
paper that every ideal of R is isomorphic to a trace ideal if and only if R is
an artinian Gorenstein ring, or a 1-dimensional hypersurface with multiplicity
at most 2, or a unique factorization domain.
