Note on the divisoriality of domains of the form k[[Xp,Xq]]k[[Xp,Xq]]k[[X^{p}, X^{q}]], k[Xp,Xq]k[Xp,Xq]k[X^{p}, X^{q}], k[[Xp,Xq,Xr]]k[[Xp,Xq,Xr]]k[[X^{p}, X^{q}, X^{r}]], and k[Xp,Xq,Xr]k[Xp,Xq,Xr]k[X^{p}, X^{q}, X^{r}]

Abdeslam MIMOUNI

Article Details

Note on the divisoriality of domains of the form k[[Xp,Xq]]k[[Xp,Xq]]k[[X^{p}, X^{q}]], k[Xp,Xq]k[Xp,Xq]k[X^{p}, X^{q}], k[[Xp,Xq,Xr]]k[[Xp,Xq,Xr]]k[[X^{p}, X^{q}, X^{r}]], and k[Xp,Xq,Xr]k[Xp,Xq,Xr]k[X^{p}, X^{q}, X^{r}]

Authors:

Abdeslam MIMOUNI

Publisher:

TUBITAK

Main Topics:

Mathematics

Journal:

Turkish Journal of Mathematics 2016 Vol.40 Issue 1, pp.38-42

Document Type:

Article

Publication Date:

1/2016

Document Language:

English

Document ID (Org No.):

2000747047

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Abstract:

 

Let kkk be a field and XXX an indeterminate over kkk. In this note we prove that the domain k[[Xp,Xq]]k[[Xp,Xq]]k[[X^{p}, X^{q}]] (resp. k[Xp,Xq]k[Xp,Xq]k[X^{p}, X^{q}]) where p,qp,qp, q are relatively prime positive integers is always divisorial but k[[Xp,Xq,Xr]]k[[Xp,Xq,Xr]]k[[X^{p}, X^{q}, X^{r}]] (resp. k[Xp,Xq,Xr]k[Xp,Xq,Xr]k[X^{p}, X^{q}, X^{r}]) where p,q,rp,q,rp, q, r are positive integers is not. We also prove that k[[Xq,Xq+1,Xq+2]]k[[Xq,Xq+1,Xq+2]]k[[X^{q}, X^{q+1}, X^{q+2}]] (resp. k[Xq,Xq+1,Xq+2]k[Xq,Xq+1,Xq+2]k[X^{q}, X^{q+1}, X^{q+2}]) is divisorial if and only if qqq 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.

Article Details

Note on the divisoriality of domains of the form k[[Xp,Xq]]k[[Xp,Xq]]k[[X^{p}, X^{q}]], k[Xp,Xq]k[Xp,Xq]k[X^{p}, X^{q}], k[[Xp,Xq,Xr]]k[[Xp,Xq,Xr]]k[[X^{p}, X^{q}, X^{r}]], and k[Xp,Xq,Xr]k[Xp,Xq,Xr]k[X^{p}, X^{q}, X^{r}]

Authors: Abdeslam MIMOUNI

Publisher: TUBITAK

Main Topics: Mathematics

Journal: Turkish Journal of Mathematics 2016 Vol.40 Issue 1, pp.38-42

Document Type: Article

Publication Date: 1/2016

Document Language: English

Document ID (Org No.): 2000747047

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Issues

Authors:

Abdeslam MIMOUNI

Publisher:

TUBITAK

Main Topics:

Mathematics

Journal:

Turkish Journal of Mathematics 2016 Vol.40 Issue 1, pp.38-42

Document Type:

Article

Publication Date:

1/2016

Document Language:

English

Document ID (Org No.):

2000747047

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098