On (quasi-)morphic property of skew polynomial rings
The main objective of this paper is to study (quasi-)morphic property of skew polynomial rings. Let $R$ be a ring, $\sigma$ be a ring homomorphism on $R$ and $n\geq 1$. We show that $R$ inherits the quasi-morphic property from $R[x;\sigma]/(x^{n+1})$. It is also proved that the morphic property over $R[x;\sigma]/(x^{n+1})$ implies that $R$ is a regular ring. Moreover, we characterize a unit-regular ring $R$ via the morphic property of $R[x;\sigma]/(x^{n+1})$. We also investigate the relationship between strongly regular rings and centrally morphic rings. For instance, we show that for a domain $R$, $R[x;\sigma]/(x^{n+1})$ is (left) centrally morphic if and only if $R$ is a division ring and $\sigma(r)=u^{-1}ru$ for some $u\in R$. Examples which delimit and illustrate our results are provided.
Keywords:
Centrally morphic ring, idempotent, morphic ring, quasi-morphic ring, regular ring, strongly regular ring unit-regular ring,
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- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI
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