The set of distances in seminormal weakly Krull monoids

Geroldinger, Alfred; Zhong, Qinghai

doi:10.1016/j.jpaa.2016.05.009

Cited by 11 publications

(3 citation statements)

References 26 publications

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“…We mention two results valid for special classes of C-domains. There is a characterization of half-factoriality for orders in quadratic number fields in number theoretic terms ([10, Theorem 3.7.15]) and for a class of seminormal weakly Krull domains (including seminormal orders in number fields) in algebraic terms involving the v-class group and extension properties of prime divisorial ideals (see [11,Theorem 6.2] and [13]).…”

Section: A Characterization Of Half-factorialitymentioning

confidence: 99%

A characterization of seminormal C-monoids

Geroldinger

Zhong

2019

Boll Unione Mat Ital

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It is well-known that a C-monoid is completely integrally closed if and only if its reduced class semigroup is a group and if this holds, then the C-monoid is a Krull monoid and the reduced class semigroup coincides with the usual class group of Krull monoids. We prove that a C-monoid is seminormal if and only if its reduced class semigroup is a union of groups. Based on this characterization we establish a criterion (in terms of the class semigroup) when seminormal C-monoids are half-factorial.2010 Mathematics Subject Classification. 20M13, 13A05, 13A15, 13F05, 13F45.

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Section: A Characterization Of Half-factorialitymentioning

confidence: 99%

A characterization of seminormal C-monoids

Geroldinger

Zhong

2019

Boll Unione Mat Ital

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“…For every finite set C ⊂ N ≥2 , there is a finitely generated Krull monoid H 1 and, if max C ≥ 3, a numerical monoid H 2 such that Ca(H 1 ) = Ca(H 2 ) = C ( [36,10]). On the other hand, sets of distances and sets of catenary degrees are intervals for transfer Krull monoids over finite groups and for classes of seminormal weakly Krull monoids ( [21,18]). The main result (Theorem 5.1) of the present section states that the set of distances and the set of catenary degrees of B(D 2n ) are intervals.…”

Section: On the Set Of Distances And The Set Of Catenary Degreesmentioning

confidence: 99%

On product-one sequences over dihedral groups

Geroldinger

Grynkiewicz

et al. 2019

Preprint

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Let G be a finite group. A sequence over G means a finite sequence of terms from G, where repetition is allowed and the order is disregarded. A product-one sequence is a sequence whose elements can be ordered such that their product equals the identity element of the group. The set of all product-one sequences over G (with concatenation of sequences as the operation) is a finitely generated C-monoid. Product-one sequences over dihedral groups have a variety of extremal properties. This article provides a detailed investigation, with methods from arithmetic combinatorics, of the arithmetic of the monoid of product-one sequences over dihedral groups.

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“…2. For every divisor-closed submonoid S ⊂ H with v p (a H) = 0 for all a ∈ S and all p ∈ P * , there is a subset G * Item 2 is of interest when studying the set * (H ) of minimal distances of H (see Remark 3.10 and[24]).…”

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confidence: 99%