Geodesic
PRINCIPAL RINGS WITH THE DUAL OF THE ISOMORPHISM THEOREM
Glasgow mathematical journal, Tome 46 (2004) no. 1, pp. 181-191

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DOI

A ring $R$ satisfies the dual of the isomorphism theorem if $R/Ra\cong \mathtt{l}(a)$ for every element $a\in R.$ 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.
DOI : 10.1017/S0017089503001654
Mots-clés : Primary 16E50, secondary 16U99, 16S70 
NICHOLSON, W. K.; CAMPOS, E. SÁNCHEZ. PRINCIPAL RINGS WITH THE DUAL OF THE ISOMORPHISM THEOREM. Glasgow mathematical journal, Tome 46 (2004) no. 1, pp. 181-191. doi: 10.1017/S0017089503001654
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