Abstract
Let D⊆E be an extension of integral domains, Γ be a nonzero torsion-free (additive) grading monoid with quotient group G such that Γ∩-Γ={0}. Set Γ *=Γ\{0} and R=D+E[Γ *]. In this paper, we show that if G satisfies the ascending chain condition on cyclic subgroups, then R is a generalized Krull domain (resp., generalized unique factorization domain) if and only if D=E, D is a generalized Krull domain (resp., generalized unique factorization domain) and Γ is a generalized Krull semigroup (resp., weakly factorial GCD-semigroup).
Original language | English |
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Pages (from-to) | 20-25 |
Number of pages | 6 |
Journal | Journal of Algebra |
Volume | 357 |
DOIs | |
State | Published - 1 May 2012 |
Keywords
- D+E[Γ ]
- Generalized Krull domain