On transfer Krull monoids

Abstract Let H be a cancellative commutative monoid, let $$\mathcal {A}(H)$$ A ( H ) the set of atoms and $$\widetilde{H}$$ ~ root closure . Then is called transfer Krull if there exists homomorphism from into monoid. It well known that both half-factorial monoids are monoids. In spite many examples counterexamples (that neither nor half-factorial), have not been studied systematically (so far) as objects on their own. The main goal present paper to attempt first in-depth study We investigate how monoid can affect property under what circumstances or Krull. particular, we show DVM, then only $$H\subseteq \widetilde{H}$$ ? inert. Moreover, prove factorial, {A}(\widetilde{H})=\{u\varepsilon \mid u\in \mathcal {A}(H),\varepsilon \in \widetilde{H}^{\times }\}$$ = { u ? ? ? , × } also half-factorial, {A}(H)\subseteq {A}(\widetilde{H})$$ Finally, point out characterizing more intricate for whose This done by providing series involving reduced affine