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Full-Text Articles in Physical Sciences and Mathematics
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 $K[X^{P}, X^{Q}, X^{R}]$, Abdeslam Mimouni
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 $K[X^{P}, X^{Q}, X^{R}]$, Abdeslam Mimouni
Turkish Journal of Mathematics
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 …
On A Question About Almost Prime Ideals, Esmaeil Rostami, Reza Nekooei
On A Question About Almost Prime Ideals, Esmaeil Rostami, Reza Nekooei
Turkish Journal of Mathematics
In this paper, by giving an example we answer positively the question ``Does there exist a $P$-primary ideal $I$ in a Noetherian domain $R$ such that $PI = I^2$, but $I$ is not almost prime?", asked by S. M. Bhatwadekar and P. K. Sharma. We also investigated conditions under which the answer to the above mentioned question is negative.