# A characterization of finite abelian groups via sets of lengths in transfer Krull monoids

@article{Zhong2018ACO, title={A characterization of finite abelian groups via sets of lengths in transfer Krull monoids}, author={Qinghai Zhong}, journal={Communications in Algebra}, year={2018}, volume={46}, pages={4021 - 4041} }

ABSTRACT Let H be a transfer Krull monoid over a finite abelian group G (for example, rings of integers, holomorphy rings in algebraic function fields, and regular congruence monoids in these domains). Then each nonunit a∈H can be written as a product of irreducible elements, say , and the number of factors k is called the length of the factorization. The set L(a) of all possible factorization lengths is the set of lengths of a. It is classical that the system ℒ(H) = {L(a)∣a∈H} of all sets of…

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