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| Paper IPM / M / 17092 |
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| Abstract: | |
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A commutative ring R has the unique decomposition into ideals
(UDI) property if for any R-module that decomposes into a fi nite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism classes of the indecomposable ideals. In [Goeters, P., Olberding, B. 2001. Unique decomposition into ideals for Noetherian Domains", Journal of Pure and Applied Algebra, 165, 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 w-ideals.
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