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Paper IPM / M / 532  


Abstract:  
Let R be a commutative Noetherian ring and let M be a finite
(i.e., finitely generated) Rmodule. The grade of M was
introduced by Rees as the least integer l ≥ 0 such that
Ext^{l}_{R}(M,R) ≠ 0. It is well known that the
grade of M is the least integer l ≥ 0 such that
Ext^{l}(M,P) ≠ 0 for some projective module P. In
this paper, we study the least integer l ≥ 0 such that
Ext^{l}(M,F) ≠ 0 for some flat Rmodule 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.
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