Ulrich ideals and modules

DOI10.1017/S0305004113000571zbMath1295.13018arXiv1206.3197OpenAlexW2129227111MaRDI QIDQ5408755

Ken-ichi Yoshida, Ryo Takahashi, Shiro Goto, Kazuho Ozeki, Kei- ichi Watanabe

Publication date: 11 April 2014

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.3197

zbMATH Keywords

Cohen-Macaulay ringsfree resolutionsUlrich modulesUlrich ideal

Mathematics Subject Classification ID

Syzygies, resolutions, complexes and commutative rings (13D02) Cohen-Macaulay modules (13C14)

Related Items (20)

On reflexive and 𝐼-Ulrich modules over curve singularities ⋮ Rings with canonical reductions ⋮ Good ideals and \(p_g\)-ideals in two-dimensional normal singularities ⋮ Ulrich ideals and 2-AGL rings ⋮ Sectional genera of parameter ideals ⋮ The Auslander-Reiten conjecture for certain non-Gorenstein Cohen-Macaulay rings ⋮ On the theory of generalized Ulrich modules ⋮ Reflexive modules over the endomorphism algebras of reflexive trace ideals ⋮ On the reducing projective dimension over local rings ⋮ On the vanishing of the theta invariant and a conjecture of Huneke and Wiegand ⋮ Resolving subcategories closed under certain operations and a conjecture of Dao and Takahashi ⋮ Poincaré series of fiber products and weak complete intersection ideals ⋮ The structure of Ulrich ideals in hypersurfaces ⋮ Ulrich modules over cyclic quotient surface singularities ⋮ The structure of chains of Ulrich ideals in Cohen-Macaulay local rings of dimension one ⋮ Ulrich ideals and almost Gorenstein rings ⋮ Residually faithful modules and the Cohen-Macaulay type of idealizations ⋮ On delta invariants and indices of ideals ⋮ Ulrich ideals in numerical semigroup rings of small multiplicity ⋮ Irreducible multiplicity and Ulrich modules

Cites Work

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• Hilbert functions of filtered modules
• Gorenstein rings and modules with high numbers of generators
• On graded rings. I
• Cohen-Macaulay local rings of maximal embedding dimension
• Ideals generated by \(R\)-sequences
• Der kanonische Modul eines Cohen-Macaulay-Rings. (The canonical moduls of a Cohen-Macaulay-ring)
• Good ideals in Gorenstein local rings
• Maximally generated Cohen-Macaulay modules.
• Form rings and regular sequences
• The homological degree of a module
• Some Examples of one Dimensional Gorenstein Domains

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