The Interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmetic Combinatorics

DOI10.1007/978-3-319-38855-7_3zbMath1349.13014arXiv1505.06059OpenAlexW216578597MaRDI QIDQ2826738

Kálmán Cziszter, Alfred Geroldinger, Matyas Domokos

Publication date: 18 October 2016

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.06059

zbMATH Keywords

Davenport constantinvariant ringsKrull monoidszero-sum sequenceNoether numberproduct one sequences

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Actions of groups on commutative rings; invariant theory (13A50) Ideals and multiplicative ideal theory in commutative rings (13A15) Sequences (mod (m)) (11B50) Arithmetic theory of semigroups (20M13)

Related Items (33)

On a conjecture of the small Davenport constant for finite groups ⋮ A generalization of Kruyswijk-Olson theorem on Davenport constant in commutative semigroups ⋮ Noether bound for invariants in relatively free algebras. ⋮ On product-one sequences over dihedral groups ⋮ An asymptotically tight bound for the Davenport constant ⋮ On product-one sequences with congruence conditions over non-abelian groups ⋮ Monoids of sequences over finite abelian groups defined via zero-sums with respect to a given set of weights and applications to factorizations of norms of algebraic integers ⋮ On monoids of weighted zero-sum sequences and applications to norm monoids in Galois number fields and binary quadratic forms ⋮ ON THE ARITHMETIC OF MORI MONOIDS AND DOMAINS ⋮ On product-one sequences over subsets of groups ⋮ The Main Zero-Sum Constants over \({\boldsymbol{D}}\) _2n \({\boldsymbol{\times C_2}}\) ⋮ Separating monomials for diagonalizable actions ⋮ On zero-sum free sequences contained in random subsets of finite cyclic groups ⋮ On the algebraic and arithmetic structure of the monoid of product-one sequences ⋮ On Erdős-Ginzburg-Ziv inverse theorems for dihedral and dicyclic groups ⋮ On monoids of plus-minus weighted zero-sum sequences: the isomorphism problem and the characterization problem ⋮ On Syzygies for Rings of Invariants of Abelian Groups ⋮ A unifying look at zero-sum invariants ⋮ Erdős-Ginzburg-Ziv theorem and Noether number for \(C_m \ltimes_\varphi C_{mn}\) ⋮ The Erdős–Burgess constant of the multiplicative semigroup of a factor ring of 𝔽q[x] ⋮ The Noether number of p-groups ⋮ Harborth constants for certain classes of metacyclic groups ⋮ On an inverse problem of Erdős, Kleitman, and Lemke ⋮ A characterization of seminormal C-monoids ⋮ The Noether numbers and the Davenport constants of the groups of order less than 32 ⋮ On congruence half-factorial Krull monoids with cyclic class group ⋮ Unnamed Item ⋮ Structure of long idempotent-sum-free sequences over finite cyclic semigroups ⋮ A Reciprocity on Finite Abelian Groups Involving Zero-Sum Sequences ⋮ Lower bounds on the Noether number ⋮ On the class semigroup of root-closed weakly Krull Mori monoids ⋮ On the invariant $\mathsf E(G)$ for groups of odd order ⋮ Degree bound for separating invariants of abelian groups

Cites Work

• Unnamed Item
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• On the generalized Davenport constant and the Noether number
• The large Davenport constant. II: General upper bounds.
• The Noether number of the non-abelian group of order \(3p\)
• The Noether number for the groups with a cyclic subgroup of index two
• Zero-separating invariants for finite groups
• Relative invariants, ideal classes and quasi-canonical modules of modular rings of invariants
• On the Davenport constant and on the structure of extremal zero-sum free sequences
• Monoids of modules and arithmetic of direct-sum decompositions.
• Groups with large Noether bound
• On the Erdős-Ginzburg-Ziv constant of finite abelian groups of high rank
• Remarks on a generalization of the Davenport constant
• The Erdős-Ginzburg-Ziv theorem for finite solvable groups.
• The Noether numbers for cyclic groups of prime order
• Zero-sum problems in finite Abelian groups: a survey
• Degree bounds -- an invitation to postmodern invariant theory
• Arithmetic of Mori domains and monoids
• Invariant polynomials and minimal zero sequences
• Separating invariants
• Relative invariants of finite groups
• Invariants of finite groups over fields of characteristic \(p\)
• Sharpening the generalized Noether bound in the invariant theory of finite groups.
• Direct sum decompositions of modules, semilocal endomorphism rings, and Krull monoids
• Noether's bound for polynomial invariants of finite groups
• The Erdős-Ginzburg-Ziv theorem for finite nilpotent groups
• The large Davenport constant. I: Groups with a cyclic, index 2 subgroup.
• Non-commutative Krull monoids: a divisor theoretic approach and their arithmetic.
• The Erdős-Ginzburg-Ziv theorem for dihedral groups.
• Long zero-free sequences in finite cyclic groups.
• Improving the Erdős-Ginzburg-Ziv theorem for some non-Abelian groups.
• Two zero-sum invariants on finite abelian groups
• Inverse zero-sum problems and algebraic invariants
• Inverse zero-sum problems II
• HIGHER-ORDER CLASS GROUPS AND BLOCK MONOIDS OF KRULL MONOIDS WITH TORSION CLASS GROUP
• A generalization of Davenport's constant and its arithmetical applications
• Direct-sum decompositions of modules with semilocal endomorphism rings
• On the distribution of algebraic numbers with prescribed factorization properties
• On The Critical Number of Finite Groups (II)
• ON v-MAROT MORI RINGS AND C-RINGS
• Invariants of Finite Groups Generated by Reflections
• The Noether bound in invariant theory of finite groups
• Some remarks on Davenport constant

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