Commutative Algebra 150 Years with Roger and Sylvia Wiegand
This volume contains the combined Proceedings of the Second International Meeting on Commutative Algebra and Related Areas (SIMCARA) held from July 22-26, 2019, at the Universidade de São Paulo, São Carlos, Brazil, and the AMS Special Session on Commutative Algebra, held from September 14-15, 2019,...
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| Hauptverfasser: | , , |
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
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American Mathematical Society
2021
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| Ausgabe: | 1 |
| Schlagworte: | |
| ISBN: | 9781470456016, 147045601X |
| Online-Zugang: | Volltext |
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Inhaltsangabe:
- Acknowledgment -- References -- Cardinalities of prime spectra of precompletions -- 1. Introduction -- 2. Cardinalities of domain precompletions -- 3. Cardinalities of spectra of domain precompletions -- 4. Precompletions with mixed cardinality spectra -- Acknowledgments -- References -- Ascent properties for test modules -- 1. Introduction -- 2. Derived categories and semidualizing complexes -- 3. Test complexes and ring homomorphisms of finite flat dimension -- 4. PD-test results -- 5. G-Dim-Test results -- Acknowledgments -- References -- Notes on endomorphisms, local cohomology and completion -- 1. Introduction -- 2. Preliminaries and the truncation complex -- 3. Endomorphisms of Local cohomology -- 4. Endomorphisms of modules -- 5. Relation to completions -- 6. A generalization -- 7. Examples -- Acknowledgment -- References -- Reducibility of parameter ideals in low powers of the maximal ideal -- 1. Introduction -- 2. A bound in dimension one -- 3. A bound in higher dimensions -- Acknowledgments -- References -- An upper bound for the first Hilbert coefficient of Gorenstein algebras and modules -- 1. Introduction -- 2. Notation -- 3. Upper bound for ₁ -- Acknowledgments -- References -- Generalized Hilbert-Kunz function of the Rees algebra of the face ring of a simplicial complex -- 1. Introduction -- 2. Preliminaries -- 3. The generalized Hilbert-Kunz function of ( , ) -- 4. Examples -- 5. Macaulay2 code for Cohen-Macaulay Stanley-Reisner rings -- Acknowledgment -- References -- Back Cover
- Cover -- Title page -- Contents -- Two conferences -- The life and times of Roger and Sylvia Wiegand -- The mathematics of Sylvia and Roger Wiegand -- Bibliography -- On an example concerning the second rigidity theorem -- 1. Introduction -- 2. Preliminaries -- 3. Main theorem -- 4. Proof of Theorem 1.2 and further remarks -- Acknowledgments -- References -- Dimension of finite free complexes over commutative Noetherian rings -- Introduction -- Dimension -- References -- Examples of multiplicities and mixed multiplicities of filtrations -- 1. Introduction -- 2. Anti-positive intersection products -- 3. Intersection theory on projective varieties -- 4. An example -- References -- Tate resolutions and MCM approximations -- Introduction -- 1. Duality in the Tate resolution of a Cohen-Macaulay module -- 2. The case of two regular sequences -- References -- The Étale locus in complete local rings -- Acknowledgments -- References -- Extensions of primes, flatness, and intersection flatness -- 1. Introduction -- 2. Basic properties -- 3. Flatness -- 4. A counterexample when a quasilocal ring has infinitely many minimal primes -- 5. Intersection flatness -- Acknowledgments -- References -- -dimension for modules over a local ring -- 1. Introduction -- 2. -dimension -- 3. Comparison to complete intersection dimension -- Acknowledgment -- References -- ℎ-local Rings -- 1. Introduction and main theorem -- 2. Proof of the main theorem -- 3. Open questions -- References -- Magic squares of squares over a finite field -- 1. Introduction -- 2. Resulting ideal of the polynomial system and its Gröbner basis -- 3. Possible degrees of ∈ _{ } and deg( _{ }) -- 4. Construction of MSS using consecutive quadratic residues -- 5. Conclusions and future directions -- References -- A generalization of coefficient ideals -- 1. Introduction -- 2. Coefficient ideals