Abstract
A ring R is called left morphic if R / R a ≅ l ( a ) for every a ∈ R . A left and right morphic ring is called a morphic ring. If M n ( R ) 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 ] / ( x n ) is strongly morphic for all n ≥ 1 iff R [ x ] / ( x 2 ) 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.
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