Krull-Schmidt theorems in dimension 1

DOI10.1090/S0002-9947-96-01619-4zbMath0858.16016OpenAlexW2148282974MaRDI QIDQ4715114

Lawrence S. Levy, Charles J. Odenthal

Publication date: 15 December 1996

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-96-01619-4

zbMATH Keywords

finitely generated modulesprimitive idempotentsKrull-Schmidt propertygenusnormalizationssemisimple Artinian ringslocal endomorphism ringsclassical orderscommutative Noetherian rings of Krull dimension oneexceptional ordersmodule-finite semiprime algebrasring-indecomposable central orders

Mathematics Subject Classification ID

Representations of orders, lattices, algebras over commutative rings (16G30) Commutative Noetherian rings and modules (13E05) Noncommutative local and semilocal rings, perfect rings (16L30) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Noetherian rings and modules (associative rings and algebras) (16P40) Localization and associative Noetherian rings (16P50)

Related Items (14)

Unnamed Item ⋮ Lattices over Bass rings and graph agglomerations ⋮ Cancellation of finite-dimensional Noetherian modules ⋮ A Krull-Schmidt theorem for one-dimensional rings of finite Cohen-Macaulay type ⋮ Unique decomposition into ideals for commutative Noetherian rings ⋮ Monoids of torsion-free modules over rings with finite representation type ⋮ Monoids of modules over rings of infinite Cohen-Macaulay type ⋮ The Krull-Schmidt property for ideals and modules over integral domains. ⋮ When Summands of Completely Decomposable Modules Are Completely Decomposable ⋮ Unique decompositions into ideals for noetherian domains. ⋮ Direct Sum Decompositions Over Two-Dimensional Local Domains ⋮ Ranks of Indecomposable Modules over Rings of Infinite Cohen-Macaulay Type ⋮ On the krull-schmidt-azumaya theorem for integral group rings ⋮ Generalized lattices over one-dimensional Noetherian domains

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