On (quasi-)morphic property of skew polynomial rings

Najmeh DEHGHANI

doi:https://doi.org/10.24330/ieja.1102387

Makale detayları

On (quasi-)morphic property of skew polynomial rings

Yazarlar:

Najmeh DEHGHANI

Yayıncı:

Abdullah HARMANCI

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Algebra 2022 Vol.32 Issue 32, pp.141-156

Belge Tipi:

Makale

Yayın Tarihi:

7/2022

Belge Dili:

İngilizce

Document ID (Org No.):

2000717759

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.1102387

Özet:

 

The  main objective of  this paper is to study  (quasi-)morphic property of skew polynomial rings. Let RRR be a ring, σσ\sigma  be  a ring homomorphism on RRR and n≥1n≥1n\geq 1. We show that RRR inherits the quasi-morphic property  from R[x;σ]/(xn+1)R[x;σ]/(xn+1)R[x;\sigma]/(x^{n+1}).
It is also proved that the morphic property over R[x;σ]/(xn+1)R[x;σ]/(xn+1)R[x;\sigma]/(x^{n+1}) implies that  RRR is a regular ring.   Moreover, we characterize a unit-regular ring RRR via  the morphic property of  R[x;σ]/(xn+1)R[x;σ]/(xn+1)R[x;\sigma]/(x^{n+1}).  We also investigate the relationship  between strongly regular rings and centrally morphic rings. For instance, we show that for  a  domain RRR,   R[x;σ]/(xn+1)R[x;σ]/(xn+1)R[x;\sigma]/(x^{n+1})  is (left) centrally morphic if and only if RRR is a division ring and σ(r)=u−1ruσ(r)=u−1ru\sigma(r)=u^{-1}ru for some u∈Ru∈Ru\in R. Examples which delimit and illustrate our results are provided.

Makale detayları

On (quasi-)morphic property of skew polynomial rings

Yazarlar: Najmeh DEHGHANI

Yayıncı: Abdullah HARMANCI

Ana Başlıklar: Matematik

Dergi: International Electronic Journal of Algebra 2022 Vol.32 Issue 32, pp.141-156

Belge Tipi: Makale

Yayın Tarihi: 7/2022

Belge Dili: İngilizce

Document ID (Org No.): 2000717759

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

DOI: https://doi.org/10.24330/ieja.1102387

Sayı

Yazarlar:

Najmeh DEHGHANI

Yayıncı:

Abdullah HARMANCI

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Algebra 2022 Vol.32 Issue 32, pp.141-156

Belge Tipi:

Makale

Yayın Tarihi:

7/2022

Belge Dili:

İngilizce

Document ID (Org No.):

2000717759

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.1102387