Remarks on module-finite pairs
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Let R ⊊ T be an extension of commutative rings having the same identity. A. Wadsworth (10) studies the situation when R and T are integral domains, and all rings between R and T are Noetherian. In this case (R, T) is called a Noetherian pair. In a similar vein, E. Davis (4) studies normal pairs and I. Papick (8) shows when coherent pairs are Noetherian pairs.
[1] I. Papick,et al. When is $D+M$ coherent? , 1976 .
[2] A. Wadsworth. Pairs of domains where all intermediate domains are Noetherian , 1974 .
[3] E. Davis. Overrings of commutative rings. III. Normal pairs , 1973 .
[4] W. Vasconcelos. Annihilators of modules with a finite free resolution , 1971 .
[5] M. E. Harris. Some results on coherent rings , 1966 .