Commutative orders whose lattices are direct sums of ideals

DOI10.1016/0022-4049(88)90002-3zbMath0653.13006OpenAlexW1995103886MaRDI QIDQ1107581

Lawrence S. Levy, Jeremy Haefner

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0022-4049(88)90002-3

zbMATH Keywords

Bass ring\(\Sigma \) I ringdirect sum of idealsfinite generation of idealsR-lattice

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) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05)

Related Items

Bounds for one-dimensional rings of finite Cohen-Macaulay type ⋮ Irreducible maps of commutative rings ⋮ Direct sum behavior of lattices over sigma-I rings ⋮ Ranks of indecomposable modules over one-dimensional rings ⋮ Indecomposable modules over one-dimensional noetherian rings ⋮ On Gorenstein orders ⋮ Direct sums of ideals ⋮ Ranks of indecomposable modules over one-dimensional rings. II ⋮ Curve singularities of finite Cohen-Macaulay type ⋮ Rank-sets of indecomposable modules over one-dimensional rings ⋮ Commutative group rings of finite representation type ⋮ Local Orders whose Lattices are Direct Sums of Ideals ⋮ Bounds for indecomposable torsion-free modules ⋮ Integral representations of groups of square-free order ⋮ One-dimensional rings of finite Cohen-Macaulay type ⋮ Torsion-free modules over reduced Witt rings ⋮ Computing abelian varieties over finite fields isogenous to a power ⋮ On local orders ⋮ Rings with two-generated ideals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the two generator problem for the ideals of a one-dimensional ring
• Dedekind-like behavior of rings with 2-generated ideals
• On the structure of principal ideal rings
• On the ubiquity of Gorenstein rings
• Some indecomposable group representations
• Torsion Free and Projective Modules

This page was built for publication: Commutative orders whose lattices are direct sums of ideals