# 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}
}
• Qinghai Zhong
• Published 15 November 2017
• Mathematics, Medicine
• Communications in Algebra
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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