On half-factoriality of transfer Krull monoids

  title={On half-factoriality of transfer Krull monoids},
  author={Weidong Gao and Chao Liu and Salvatore Tringali and Qinghai Zhong},
  journal={Communications in Algebra},
  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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Factorizations in Bounded Hereditary Noetherian Prime Rings
  • Daniel Smertnig
  • Mathematics
    Proceedings of the Edinburgh Mathematical Society
  • 2018
Abstract If H is a monoid and a = u1 ··· uk ∈ H with atoms (irreducible elements) u1, … , uk, then k is a length of a, the set of lengths of a is denoted by Ⅼ(a), and ℒ(H) = {Ⅼ(a) | a ∈ H} is the
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