The Extensional Structure of Commutative Noetherian Rings

DOI10.1081/AGB-120021881zbMath1020.13005OpenAlexW2087918772MaRDI QIDQ4408720

Gary Brookfield

Publication date: 29 June 2003

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/agb-120021881

zbMATH Keywords

finitely generated modulesmultiplicitiesideal class groupsubmodule seriesminimal associated prime ideals

Mathematics Subject Classification ID

Commutative Noetherian rings and modules (13E05) Structure, classification theorems for modules and ideals in commutative rings (13C05) Commutative rings and modules of finite generation or presentation; number of generators (13E15) Class groups (13C20)

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The Jordan-Hölder property and Grothendieck monoids of exact categories

Cites Work

• Krull-Schmidt uniqueness fails dramatically over subrings of Z\(\oplus\dots \oplus Z\)
• Primely generated regular refinement monoids
• Injective positively ordered monoids. I
• Separative cancellation for projective modules over exchange rings
• Embedding simple commutative monoids into simple refinement monoids
• Direct sum cancellation of Noetherian modules
• Refinement monoids, Vaught monoids, and Boolean algebras
• The dimension monoid of a lattice
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