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Rings, polynomials, and modules

Author: Marco Fontana; Sophie Frisch; Sarah Glaz; Francesca Tartarone; Paolo Zanardo
Publisher: Cham : Springer, 2017.
Edition/Format:   eBook : Document : Conference publication : EnglishView all editions and formats
Summary:
This volume presents a collection of articles highlighting recent developments in commutative algebra and related non-commutative generalizations. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are  Read more...
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Genre/Form: Electronic books
Conference papers and proceedings
Congresses
Additional Physical Format: Print version:
Fontana, Marco.
Rings, Polynomials, and Modules.
Cham : Springer International Publishing, ©2017
Material Type: Conference publication, Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Marco Fontana; Sophie Frisch; Sarah Glaz; Francesca Tartarone; Paolo Zanardo
ISBN: 9783319658742 3319658743 3319658727 9783319658728
OCLC Number: 1012347554
Notes: 4 The Scheme of Semisimple Representations of A.
Description: 1 online resource (374 pages)
Contents: Preface; Contents; Reducing Fractions to Lowest Terms; References; Unique Factorization in Torsion-Free Modules; 1 Introduction; 2 Preliminaries; 3 Atomic and Factorable Modules; 4 Factorable Modules over Factorial Domains; 5 Factorable Ring Extensions; 6 Notes; References; n-Absorbing Ideals of Commutative Rings and Recent Progress on Three Conjectures: A Survey; 1 Introduction; 2 Basic Properties of n-Absorbing Ideals; 3 Extensions of n-Absorbing Ideals; 4 n-Absorbing Ideals in Specific Rings; 5 Strongly n-Absorbing Ideals and Recent Progresses on Three Conjectures. 6 n-Krull Dimension of Commutative Rings7 (m, n)-Closed Ideals and Quasi-n-Absorbing Ideals; 8 2-Absorbing Primary Ideals of Commutative Rings; References; Embedding Dimension and Codimension of Tensor Products of Algebras over a Field; 1 Introduction; 2 Embedding Dimension of Noetherian Local Rings; 3 Embedding Dimension and Codimension of Polynomial Rings; 4 Embedding Dimension and Codimension of Tensor Products Issued from Separable Extension Fields; 5 Embedding Dimension and Codimension of Tensor Products of Algebras with Separable Residue Fields; References. Minimal Generating Sets for the D-Algebra Int(S, D)1 Introduction; 2 Minimal Generating Sets for the Z-Algebra Int(Zp); 2.1 Extracted from the Regular Basis Formed by the eepic()Xn; 2.2 Extracted from the Basis Formed by the Fermat Polynomials; 3 Generating Sets in the Local Case; 3.1 Gaps and Generating Sets; 3.2 Structural Constants; 3.3 Regular Bases Associated to v-Orderings; 4 Minimal Generating Sets in the case of a Regular Subset; 4.1 Regular Subsets, Gaps, and Strong v-Orderings; 4.2 Minimal Generating Sets Associated to Strong v-Orderings. 4.3 Other Minimal Generating Sets when S is a Regular Subset4.4 The Generating Set Associated to a Lubin-Tate Formal Group Law; 5 Globalization when D is a Dedekind Domain; 5.1 The Factorial Ideals and Their Gaps; 5.2 Localization and Globalization; 5.3 Classical Examples; 5.4 Globalization of the Sets Given by Lubin-Tate Formal Group Laws; References; Algebraic Entropy in Locally Linearly Compact Vector Spaces; 1 Introduction; 2 Background on Locally Linearly Compact Vector Spaces; 3 Existence of the Limit and Basic Properties; 4 General Properties and Examples; 5 Limit-Free Formula. 6 Addition TheoremReferences; Commutative Rings Whose Finitely Generated Ideals are Quasi-Flat; 1 Introduction; 2 Quasi-Flat Modules: Generalities; 3 Quasi-Flat Ideals Over Local fqp-Rings; 4 Quasi-Projective Ideals Over Local fqp-Rings; 5 λ-Dimension of Commutative fqf-Rings; References; Commutative Rings with a Prescribed Number of Isomorphism Classes of Minimal Ring Extensions; 1 Introduction; 2 Results; References; Applications of Multisymmetric Syzygies in Invariant Theory; 1 Introduction; 2 Generators and Relations for Symmetric Tensor Powers of a Commutative Algebra; 3 Wreath Products.
Responsibility: Marco Fontana [and others], editors.

Abstract:

This volume presents a collection of articles highlighting recent developments in commutative algebra and related non-commutative generalizations. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non-Noetherian ring theory, module theory and integer-valued polynomials along with connections to algebraic number theory, algebraic geometry, topology and homological algebra. Most of the eighteen contributions are authored by attendees of the two conferences in commutative algebra that were held in the summer of 2016: "Recent Advances in Commutative Ring and Module Theory," Bressanone, Italy; "Conference on Rings and Polynomials" Graz, Austria. There is also a small collection of invited articles authored by experts in the area who could not attend either of the conferences. Following the model of the talks given at these conferences, the volume contains a number of comprehensive survey papers along with related research articles featuring recent results that have not yet been published elsewhere.--

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