Commutative algebra : 150 years with Roger and Sylvia Wiegand / editors, Nicholas R. Baeth [et al.]

Format:

Book

Conference/Event

Contributor:

Baeth, Nicholas R., 1978- editor.

Freitas, Thiago H., editor.

Leuschke, Graham J., 1973- editor.

Pérez, Victor Hugo Jorge, editor.

Conference Name:

AMS International Meeting on Commutative Algebra and Related Areas (2nd : 2019 : Universidade de São Paulo)

Series:

Contemporary mathematics (American Mathematical Society) ; v. 773.

Contemporary mathematics ; 773

Language:

English

Subjects (All):

Wiegand, Roger, 1943---Influence.

Wiegand, Roger.

Wiegand, Sylvia--Influence.

Wiegand, Sylvia.

Commutative algebra--Congresses.

Commutative algebra.

Influence (Literary, artistic, etc.).

Physical Description:

1 online resource (xvii, 224 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, RI : American Mathematical Society, [2021]

Summary:

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, at the University of Wisconsin-Madison, Wisconsin.These two meetings celebrated the combined 150th birthday of Roger and Sylvia Wiegand. The Wiegands have been a fixture in the commutative algebra community, as well as the wider mathematical community, for over 40 years.Articles in this volume cover various areas of factorization theory, homological algebra, ideal theory, representation theory, homological rigidity, maximal Cohen-Macaulay modules, and the behavior of prime spectra under completion, as well as some topics in related fields. The volume itself bears evidence that the area of commutative algebra is a vibrant one and highlights the influence of the Wiegands on generations of researchers. It will be useful to researchers and graduate students.

Contents:

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

Examples of multiplicities and mixed multiplicities of filtrations

2. Anti-positive intersection products

3. Intersection theory on projective varieties

4. An example

Tate resolutions and MCM approximations

1. Duality in the Tate resolution of a Cohen-Macaulay module

2. The case of two regular sequences

The Étale locus in complete local rings

Extensions of primes, flatness, and intersection flatness

2. Basic properties

3. Flatness

4. A counterexample when a quasilocal ring has infinitely many minimal primes

5. Intersection flatness

-dimension for modules over a local ring

2. -dimension

3. Comparison to complete intersection dimension

Acknowledgment

ℎ-local Rings

1. Introduction and main theorem

2. Proof of the main theorem

3. Open questions

Magic squares of squares over a finite field

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

A generalization of coefficient ideals

2. Coefficient ideals.

Acknowledgment

Cardinalities of prime spectra of precompletions

2. Cardinalities of domain precompletions

3. Cardinalities of spectra of domain precompletions

4. Precompletions with mixed cardinality spectra

Ascent properties for test modules

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

Notes on endomorphisms, local cohomology and completion

2. Preliminaries and the truncation complex

3. Endomorphisms of Local cohomology

4. Endomorphisms of modules

5. Relation to completions

6. A generalization

7. Examples

Reducibility of parameter ideals in low powers of the maximal ideal

2. A bound in dimension one

3. A bound in higher dimensions

An upper bound for the first Hilbert coefficient of Gorenstein algebras and modules

2. Notation

3. Upper bound for ₁

Generalized Hilbert-Kunz function of the Rees algebra of the face ring of a simplicial complex

3. The generalized Hilbert-Kunz function of ( , )

4. Examples

5. Macaulay2 code for Cohen-Macaulay Stanley-Reisner rings

Back Cover.

Notes:

Includes bibliographical references.

This volume contains the combined Proceedings of the Second International Meeting on Commutative Algebra and Related Areas (SIMCARA) in Universidade de São Paulo, São Carlos, Brazil (July 22-26, 2019), and the AMS Special Session on Commutative Algebra: In Celebration of the 150th Birthday of Roger and Sylvia Wiegand at the Fall Central Sectional Meeting of the AMS in Madison - Wisconsin (September 14-15, 2019).

Description based on print version record.

ISBN:

1-4704-6515-9

OCLC:

1273929089