Abstract
Let D be a domain and let S be a torsion-free monoid such that D has characteristic 0 or the quotient group of S satisfies the ascending chain condition on cyclic subgroups.
We give a characterization of when the monoid algebra D[S] is weakly Krull. As corollaries, we reobtain the results on when D[S] is Krull resp. weakly factorial, due to Chouinard resp. Chang. Furthermore, we deduce a characterization of
generalized Krull monoid algebras analogous to our main result and we characterize the weakly Krull domains among the affine monoid algebras.
We give a characterization of when the monoid algebra D[S] is weakly Krull. As corollaries, we reobtain the results on when D[S] is Krull resp. weakly factorial, due to Chouinard resp. Chang. Furthermore, we deduce a characterization of
generalized Krull monoid algebras analogous to our main result and we characterize the weakly Krull domains among the affine monoid algebras.
Original language | English |
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Pages (from-to) | 277-292 |
Number of pages | 16 |
Journal | Journal of Algebra |
Volume | 590 |
DOIs | |
Publication status | Published - 2022 |
Keywords
- Affine monoid
- Affine monoid algebra
- Affine monoid ring
- Monoid algebra
- Monoid ring
- Semigroup ring
- Weakly Krull domain
- Weakly Krull monoid
ASJC Scopus subject areas
- Algebra and Number Theory
Cooperations
- NAWI Graz