Geodesic
New characterizations of approximately Gorenstein rings
Glasgow mathematical journal, Tome 34 (1992) no. 3, pp. 361-363

Voir la notice de l'article provenant de la source Cambridge University Press

In [1], a condition was sought on a commutative Noetherian ring R such that whenever R satisfied the condition and R was cyclically pure in an R-algebra S, then R was necessarily pure in S. Such a condition was found and turned out not only to be a sufficient condition but also a necessary condition. Rings satisfying this condition were called approximately Gorenstein. In this paper, we give new equivalent conditions for a ring to be approximately Gorenstein. Our conditions involve a certain metric topology defined on the lattice of ideals of a commutative Noetherian ring as well as the concept of a principal system. The notion of principal systems was defined in [9] and was suggested by Macaulay's theory of inverse systems [7]. These ideas have proved to be useful in many research probems in commutative algebra. 
Johnson, Johnny A.; Taylor, Monty B. New characterizations of approximately Gorenstein rings. Glasgow mathematical journal, Tome 34 (1992) no. 3, pp. 361-363. doi: 10.1017/S0017089500008958
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