Rings whose ideals are isomorphic to trace ideals
arXiv:1807.00291
Abstract
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.
v1: 9 pages; v2: 10 pages, some information on the Huneke-Wiegand conjecture is added