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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
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