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- W2268618185 abstract "Let $k$ be a field and $X$ an indeterminate over $k$. In this note we prove that the domain $k[[X^{p}, X^{q}]]$ (resp. $k[X^{p}, X^{q}]$) where $p, q$ are relatively prime positive integers is always divisorial but $k[[X^{p}, X^{q}, X^{r}]]$ (resp. $k[X^{p}, X^{q}, X^{r}]$) where $p, q, r$ are positive integers is not. We also prove that $k[[X^{q}, X^{q+1}, X^{q+2}]]$ (resp. $k[X^{q}, X^{q+1}, X^{q+2}]$) is divisorial if and only if $q$ is even. These are very special cases of well-known results on semigroup rings, but our proofs are mainly concerned with the computation of the dual (equivalently the inverse) of the maximal ideal of the ring." @default.
- W2268618185 created "2016-06-24" @default.
- W2268618185 creator A5006110531 @default.
- W2268618185 date "2016-01-01" @default.
- W2268618185 modified "2023-09-26" @default.
- W2268618185 title "Note on the divisoriality of domains of the form $k[[X^{p}, X^{q}]]$, $k[X^{p}, X^{q}]$, $k[[X^{p}, X^{q}, X^{r}]]$, and $k[X^{p}, X^{q}, X^{r}]$" @default.
- W2268618185 doi "https://doi.org/10.3906/mat-1503-15" @default.
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