Unique decompositions into w-ideals for strong Mori domains

Abstract

A commutative ring [Formula: see text] has the unique decomposition into ideals (UDI) property if, for any [Formula: see text]-module that decomposes into a finite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism classes of the indecomposable ideals. In [P. Goeters and B. Olberding, Unique decomposition into ideals for Noetherian domains, J. Pure Appl. Algebra 165 (2001) 169–182], the UDI property has been characterized for Noetherian integral domains. In this paper, we aim to study the UDI-like property for strong Mori domains; domains satisfying the ascending chain condition on [Formula: see text]-ideals.