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| Paper IPM / M / 531 |
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| Abstract: | |||||||
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Let R be a commutative Noetherian ring and let M be a finite
(that is, finitely generated) R-module. The notion grade of
M, grade M, has been introduced by Rees as the least
integer t ≥ 0 such that ExttR(M,R) ≠ 0, see [
11]. The Gorenstein dimension of M, G−dimM, has
been introduced by Auslander as the largest integer t ≥ 0 such
that ExttR(M,R) ≠ 0, see [3]. In this paper
the R-module M is called G-perfect if gradeM=G−dimM. It is a generalization of perfect module. We prove
several results for the new concept similar to the classical
results.
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