Unique decompositions into ideals for noetherian domains.

DOI10.1016/S0022-4049(00)00182-1zbMath1094.13526OpenAlexW2058234016MaRDI QIDQ5954072

Bruce Olberding, Pat Goeters

Publication date: 2001

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-4049(00)00182-1

Mathematics Subject Classification ID

Commutative Noetherian rings and modules (13E05) Structure, classification theorems for modules and ideals in commutative rings (13C05) Torsion-free groups, finite rank (20K15)

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Unique decompositions into regular ideals for Marot rings ⋮ Unnamed Item ⋮ Unique decomposition into ideals for commutative Noetherian rings ⋮ Unique decompositions into w-ideals for strong Mori domains ⋮ Unique decomposition into ideals for reduced commutative Noetherian rings. II. ⋮ A geometric setting for some properties of torsion-free modules. ⋮ The Krull-Schmidt property for ideals and modules over integral domains. ⋮ Unique decomposition into ideals for reduced commutative Noetherian rings

Cites Work

• Unnamed Item
• Cancellation over commutative rings of dimension one and two
• Rings with two-generated ideals
• Finite rank torsion free Abelian groups and rings
• Stable isomorphism of modules over one-dimensional rings
• 1-dimensional Cohen-Macaulay rings
• Krull-Schmidt theorems in dimension 1
• Package deal theorems and splitting orders in dimension 1
• Number fields