A Generalization of the Grade of a Module

• 来源期刊: 代数集刊（英文版）
• 关键词: perfect modules grade of modules balanced big Cohen-Macaulay modules
• 年，卷（期）: 2002,（3）
• 页码范围: 265-270
• 页数: 6页
• 语种: 英文

摘要

Let R be a commutative Noetherian ring and M a finite (i.e., finitely generated) R-module. The grade of M was introduced by Rees as the least integer l≥ 0 such that ExtlR(M, R) ≠ 0. It is well known that the grade of M is the least integer l ≥ 0 such that Extl(M, P) ≠ 0 for some projective module P. In this paper, we study the least integer l ≥ 0 such that Extl(M, F) ≠ 0 for some flat R-module F when M is not necessarily finite. This is an extension of the grade of M. Similar to the classical results, we prove several results for the new concept.