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New characterizations of approximately Gorenstein rings

Published online by Cambridge University Press:  18 May 2009

Johnny A. Johnson  and
Monty B. Taylor
Johnny A. Johnson
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3476
Monty B. Taylor
Affiliation:
Department of Mathematics and Computer Science, University of Texas-Pan American, Edinburg, TX 78539-2999
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 3 , September 1992 , pp. 361 - 363
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

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