Note on Colon-Multiplication Domains

الملخص EN

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.