On a property of the ideals of the polynomial ring R[x]R[x]R[x]

Amr Ali Abdulkader AL-MAKTRY

doi:https://doi.org/10.24330/ieja.1058380

Makale detayları

On a property of the ideals of the polynomial ring R[x]R[x]R[x]

Yazarlar:

Amr Ali Abdulkader AL-MAKTRY

Yayıncı:

Abdullah HARMANCI

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Algebra 2022 Vol.31 Issue 31, pp.1-12

Belge Tipi:

Makale

Yayın Tarihi:

1/2022

Belge Dili:

İngilizce

Document ID (Org No.):

2000717770

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.1058380

Özet:

 

Let RR be a commutative ring with unity 1≠01≠0. In this paper we introduce  the definition of the first derivative property on the ideals of  the polynomial ring R[x]R[x]. In particular,   when RR is a finite local ring with principal maximal ideal m≠{0}m≠{0}  of  index of nilpotency ee, where 1<e≤|R/m|+11≤e≤|R/m|+1,  we show that the null ideal consisting of polynomials inducing the zero function on RR  satisfies this property. As an application,  when RR  is a finite local ring with  null ideal satisfying this property,  we  prove  that the stabilizer group of RR in the group of   polynomial permutations on the ring R[x]/(x2)R[x]/(x2),  is isomorphic  to a certain factor group of the null ideal.

Makale detayları

On a property of the ideals of the polynomial ring R[x]R[x]R[x]

Yazarlar: Amr Ali Abdulkader AL-MAKTRY

Yayıncı: Abdullah HARMANCI

Ana Başlıklar: Matematik

Dergi: International Electronic Journal of Algebra 2022 Vol.31 Issue 31, pp.1-12

Belge Tipi: Makale

Yayın Tarihi: 1/2022

Belge Dili: İngilizce

Document ID (Org No.): 2000717770

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

DOI: https://doi.org/10.24330/ieja.1058380

Sayı

Yazarlar:

Amr Ali Abdulkader AL-MAKTRY

Yayıncı:

Abdullah HARMANCI

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Algebra 2022 Vol.31 Issue 31, pp.1-12

Belge Tipi:

Makale

Yayın Tarihi:

1/2022

Belge Dili:

İngilizce

Document ID (Org No.):

2000717770

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.1058380