Note on colon-multiplication domains (Q1958065)

Summary: Let \(R\) be an integral domain with quotient field \(L\). Call a nonzero (fractional) ideal \(A\) of \(R\) a colon-multiplication ideal any ideal \(A\), such that \(B(A:B)=A\) for every nonzero (fractional) ideal \(B\) of \(R\). In this note, we characterize integral domains for which every maximal ideal (resp., every nonzero ideal) is a colon-multiplication ideal. It turns that this notion unifies Dedekind and MTP domains.