27 citations · 190 across the 32 of their papers we have counts for
18 papers · 1 filter
On conductor submonoids of factorial monoids
Alfred Geroldinger, Weihao Yan, Qinghai Zhong
We study algebraic and arithmetic properties of submonoids (resp. subrings) of factorial monoids (resp. factorial domains) whose non-invertible elements all lie in the conductor. T…
On Monoids of plus-minus weighted Zero-Sum Sequences: The Isomorphism Problem and the Characterization Problem
Florin Fabsits, Alfred Geroldinger, Andreas Reinhart +1
Let be an additive abelian group. A sequence of terms from is a plus-minus weighted zero-sum sequence if there are $\varepsilon_1,\ldots,\v…
A characterization of length-factorial Krull monoids
Alfred Geroldinger, Qinghai Zhong
An atomic monoid is length-factorial if each two distinct factorizations of any element have distinct factorization lengths. We provide a characterization of length-factorial Krull…
A realization result for systems of sets of lengths
Alfred Geroldinger, Qinghai Zhong
Let be a family of finite subsets of having the following properties. (a). and all other sets of lie in…
On half-factoriality of transfer Krull monoids
Weidong Gao, Chao Liu, Salvatore Tringali +1
Let be a transfer Krull monoid over a subset of an abelian group with finite exponent. Then every non-unit can be written as a finite product of atoms, say $…
Factorization Theory in Commutative Monoids
Alfred Geroldinger, Qinghai Zhong
This is a survey on factorization theory. We discuss finitely generated monoids (including affine monoids), primary monoids (including numerical monoids), power sets with set addit…
On the arithmetic of Mori monoids and domains
Qinghai Zhong
Let be a Mori domain with complete integral closure , nonzero conductor , and suppose that both -class groups $\mathcal C_v (R…
A characterization of seminormal C-monoids
Alfred Geroldinger, Qinghai Zhong
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 th…
On elasticities of locally finitely generated monoids
Qinghai Zhong
Let be a commutative and cancellative monoid. The elasticity of a non-unit is the supremum of over all for which there are factorizations of the f…
Sets of Arithmetical Invariants in Transfer Krull Monoids
Alfred Geroldinger, Qinghai Zhong
Transfer Krull monoids are a recent concept including all commutative Krull domains and also, for example, wide classes of non-commutative Dedekind domains. We show that transfer K…
Long sets of lengths with maximal elasticity
Alfred Geroldinger, Qinghai Zhong
We introduce a new invariant describing the structure of sets of lengths in atomic monoids and domains. For an atomic monoid , let be the set of all positive integers…
Sets of minimal distances and characterizations of class groups of Krull monoids
Qinghai Zhong
Let be a Krull monoid with finite class group such that every class contains a prime divisor. Then every non-unit can be written as a finite product of atoms, say…
Systems of sets of lengths: Transfer Krull monoids versus weakly Krull monoids
Alfred Geroldinger, Wolfgang Schmid, Qinghai Zhong
Transfer Krull monoids are monoids which allow a weak transfer homomorphism to a commutative Krull monoid, and hence the system of sets of lengths of a transfer Krull monoid coinci…
The set of distances in seminormal weakly Krull monoids
Alfred Geroldinger, Qinghai Zhong
The set of distances of a monoid or of a domain is the set of all with the following property: there are irreducible elements $u_1, \ldots, u_k, v_1, \ldots, v_{k…
Products of atoms in Krull monoids
Yushuang Fan, Qinghai Zhong
Let be a Krull monoid with finite class group such that every class contains a prime divisor. For , let denote the set of all $m\in \mathb…
A characterization of class groups via sets of lengths
Alfred Geroldinger, Wolfgang Schmid
Let be a Krull monoid with class group such that every class contains a prime divisor. Then every nonunit can be written as a finite product of irreducible elemen…
The catenary degree of Krull monoids II
Alfred Geroldinger, Qinghai Zhong
Let be a Krull monoid with finite class group such that every class contains a prime divisor (for example, a ring of integers in an algebraic number field or a holomorphy r…
The set of minimal distances in Krull monoids
Alfred Geroldinger, Qinghai Zhong
Let be a Krull monoid with finite class group . Then every non-unit can be written as a finite product of atoms, say . The set $\math…