Irreducible maps of commutative rings

DOI10.1080/00927879308824573zbMath0789.16012OpenAlexW2052003671MaRDI QIDQ5966719

Jeremy Haefner

Publication date: 15 March 1993

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

Full work available at URL: https://doi.org/10.1080/00927879308824573

zbMATH Keywords

Dedekind domainalmost split sequencelocal endomorphism ringsBass ringindecomposable latticeirreducible mapcategory of \(R\)-lattices

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Structure, classification theorems for modules and ideals in commutative rings (13C05) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05)

Related Items

Pure projective torsion free modules over Bass domains ⋮ Irreducible maps of commutative rings

Cites Work

• Commutative orders whose lattices are direct sums of ideals
• Integral representations of groups of square-free order
• Dedekind-like behavior of rings with 2-generated ideals
• Modules over pullbacks and subdirect sums
• On the ubiquity of Gorenstein rings
• Local Orders whose Lattices are Direct Sums of Ideals
• Orders with loops in their auslander-reiten graph
• Irreducible maps of commutative rings
• Almost split sequences for integral group rings and orders
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