Najmeh Dehghani

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