On half-factoriality of transfer Krull monoids

@article{Gao2020OnHO,
  title={On half-factoriality of transfer Krull monoids},
  author={Weidong Gao and Chao Liu and Salvatore Tringali and Qinghai Zhong},
  journal={Communications in Algebra},
  year={2020},
  volume={49},
  pages={409 - 420}
}
Abstract Let H be a transfer Krull monoid over a subset G 0 of an abelian group G with finite exponent. Then every non-unit can be written as a finite product of atoms, say The set of all possible factorization lengths k is called the set of lengths of a, and H is said to be half-factorial if for all We show that, if is a non-unit and then the smallest divisor-closed submonoid of H containing a is half-factorial. In addition, we prove that, if G 0 is finite and then H is half-factorial. 
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<jats:p>Let <jats:italic>H</jats:italic> be a cancellative commutative monoid, let <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathcal {A}(H)$$</jats:tex-math><mml:math

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