On products of \(k\) atoms.

DOI10.1007/s00605-008-0547-zzbMath1184.20051OpenAlexW2144161970MaRDI QIDQ1027743

Weidong Gao, Alfred Geroldinger

Publication date: 30 June 2009

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-008-0547-z

zbMATH Keywords

Krull monoidsproducts of irreducible elementsnon-unique factorizationsatomic monoidscommutative cancellative semigroupssets of lengths of factorizations

Mathematics Subject Classification ID

Commutative semigroups (20M14) Units and factorization (11R27) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Divisibility and factorizations in commutative rings (13A05)

Related Items (37)

Factorization invariants of the additive structure of exponential Puiseux semirings ⋮ On the index-r-free sequences over finite cyclic groups ⋮ Unnamed Item ⋮ Products of \(k\) atoms in Krull monoids ⋮ Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids. ⋮ On the structure of n-zero-sum free sequences over cyclic groups of order n ⋮ Upper triangular matrices over information algebras ⋮ Sets of Lengths ⋮ Unnamed Item ⋮ Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules ⋮ ON THE ARITHMETIC OF MORI MONOIDS AND DOMAINS ⋮ On product-one sequences over subsets of groups ⋮ On Monoids of Ideals of Orders in Quadratic Number Fields ⋮ On strongly primary monoids, with a focus on Puiseux monoids ⋮ Indexes of long zero-sum sequences over cyclic groups ⋮ The monotone catenary degree of monoids of ideals ⋮ Solution to the index conjecture in zero-sum theory ⋮ Factorization properties of Leamer monoids. ⋮ ON THE INDEX-CONJECTURE OF LENGTH FOUR MINIMAL ZERO-SUM SEQUENCES II ⋮ MINIMAL ZERO-SUM SEQUENCES OF LENGTH FOUR OVER FINITE CYCLIC GROUPS II ⋮ Minimal zero sum sequences of length four over finite cyclic groups ⋮ Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids ⋮ On the arithmetic of tame monoids with applications to Krull monoids and Mori domains. ⋮ On the arithmetic of Krull monoids with infinite cyclic class group ⋮ Structural properties of subadditive families with applications to factorization theory ⋮ Products of two atoms in Krull monoids and arithmetical characterizations of class groups. ⋮ Minimal zero-sum sequences of length four over cyclic group with order \(n = p^{\alpha} q^{\beta}\) ⋮ Factorization theory in commutative monoids ⋮ Arithmetic of seminormal weakly Krull monoids and domains ⋮ On the arithmetic of Krull monoids with finite Davenport constant. ⋮ Some Recent Results and Open Problems on Sets of Lengths of Krull Monoids with Finite Class Group ⋮ Arithmetical characterization of class groups of the form \(\mathbb Z/n\mathbb Z\oplus\mathbb Z/n\mathbb Z\) via the system of sets of lengths. ⋮ Unions of sets of lengths. ⋮ A semigroup-theoretical view of direct-sum decompositions and associated combinatorial problems ⋮ On the class semigroup of root-closed weakly Krull Mori monoids ⋮ On a conjecture of Lemke and Kleitman ⋮ ON THE INDEX-CONJECTURE ON LENGTH FOUR MINIMAL ZERO-SUM SEQUENCES

Cites Work

• Factorization problems in semigroups
• Factorization in Dedekind domains with finite class group
• Arithmetic of Mori domains and monoids
• Unions of sets of lengths.
• On the lengths of factorizations of elements in an algebraic number ring
• Minimal zero-sequences and the strong Davenport constant
• Generalized sets of lengths
• Factorization in finitely generated domains.
• On the index of minimal zero-sum sequences over finite cyclic groups
• Long zero-free sequences in finite cyclic groups.
• Local tameness of \(v\)-Noetherian monoids.
• Unnamed Item

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