Abstract
Ar ing R satisfies the dual of the isomorphism theorem if R/Ra ∼ l(a )f or ever ye lement a ∈ R. We call these rings left morphic, and say that R is left P-morphic if, in addition, every left ideal is principal. In this paper we characterize the left and right P-morphic rings and show that they form a Morita invariant class. We also characterize the semiperfect left P-morphic rings as the finite direct products of matrix rings over left uniserial rings of finite composition length. J. Clark has an example of a commutative, uniserial ring with exactly one non-principal ideal. We show that Clark's example is (left) morphic and obtain a non-commutative analogue.
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