Morphic rings and unit regular rings

A ring R is called left morphic if image for every aset membership, variantR. A left and right morphic ring is called a morphic ring. If image is morphic for all n≥1 then R is called a strongly morphic ring. A well-known result of Erlich says that a ring R is unit regular iff it is both (von Neumann) regular and left morphic. A new connection between morphic rings and unit regular rings is proved here: a ring R is unit regular iff R[x]/(xn) is strongly morphic for all n≥1 iff R[x]/(x2) is morphic. Various new families of left morphic or strongly morphic rings are constructed as extensions of unit regular rings and of principal ideal domains. This places some known examples in a broader context and answers some existing questions.