The main goal of this research article is to study the morphic property of the quotient ring of a skew (left) polynomial ring in Formula: see text by Formula: see text. We prove that if Formula: see text is an endomorphism of a ring Formula: see text and Formula: see text then Formula: see text is von Neumann regular if Formula: see text is left morphic in Formula: see text. Using this result, it is shown that a ring Formula: see text is unit regular if Formula: see text is left morphic. Further, we prove that for any endomorphism Formula: see text of a ring Formula: see text, the ring Formula: see text is left morphic and Formula: see text is abelian if and only if Formula: see text is strongly regular and Formula: see text for all Formula: see text. Also it is shown that for any endomorphism Formula: see text of a ring Formula: see text, the ring Formula: see text is left centrally morphic if and only if Formula: see text is strongly regular and there exists Formula: see text such that Formula: see text for all Formula: see text.
Soumya et al. (Fri,) studied this question.