27 citations · 190 across the 32 of their papers we have counts for
33 papers
How iterated sumsets grow under the assumption of small doubling
Dongchun Han, Qinghai Zhong
Let be a real number and let be a finite and nonempty subset. Suppose . A fundamental open problem is to characterize the size of higher i…
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…
On monoids of weighted zero-sum sequences and applications to norm monoids in Galois number fields and binary quadratic forms
Alfred Geroldinger, Franz Halter-Koch, Qinghai Zhong
Let be an additive finite abelian group and be a subset of the endomorphism group of . A sequence ove…
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…
On clean, weakly clean, and feebly clean commutative group rings
Yuanlin Li, Qinghai Zhong
A ring is said to be clean if each element of can be written as the sum of a unit and an idempotent. is said to be weakly clean if each element of is either a sum o…
On product-one sequences over subsets of groups
Victor Fadinger, Qinghai Zhong
Let be a group and be a subset. A sequence over means a finite sequence of terms from , where the order of elements is disregarded and the repetiti…
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 a zero-sum problem arising from factorization theory
Aqsa Bashir, Alfred Geroldinger, Qinghai Zhong
We study a zero-sum problem dealing with minimal zero-sum sequences of maximal length over finite abelian groups. A positive answer to this problem yields a structural description…
Clean group rings over localizations of rings of integers
Yuanlin Li, Qinghai Zhong
A ring is said to be clean if each element of can be written as the sum of a unit and an idempotent. In a recent article (J. Algebra, 405 (2014), 168-178), Immormino and Mc…
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 $…
On product-one sequences over dihedral groups
Alfred Geroldinger, David J. Grynkiewicz, Jun Seok Oh +1
Let be a finite group. A sequence over means a finite sequence of terms from , where repetition is allowed and the order is disregarded. A product-one sequence is a sequ…
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 Erdős-Ginzburg-Ziv inverse theorems for Dihedral and Dicyclic groups
Jun Seok Oh, Qinghai Zhong
Let be a finite group and exp = lcmord. A finite unordered sequence of terms from , where repetition is allowed, is a product-one sequence if…
On minimal product-one sequences of maximal length over Dihedral and Dicyclic groups
Jun Seok Oh, Qinghai Zhong
Let be a finite group. By a sequence over , we mean a finite unordered sequence of terms from , where repetition is allowed, and we say that it is a product-one sequence…
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…
A characterization of finite abelian groups via sets of lengths in transfer Krull monoids
Qinghai Zhong
Let be a transfer Krull monoid over a finite ablian group (for example, rings of integers, holomorphy rings in algebraic function fields, and regular congruence monoids in…
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…