Relative FP-Projective Modules
Relative FP-Projective Modules
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DOI：
10.1081/agb-200061047
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发表时间：
2005-04
影响因子：
0.7
通讯作者：
L. Mao;Nanqing Ding
中科院分区：
文献类型：
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作者：
L. Mao;Nanqing Ding
设R为环，M为右R模。对于任意FP -内射维数≤n的右R -模n，若Ext 1 (M, n) = 0，则M称为n - FP -射影，其中n为非负整数或n =∞。定义ν R (M)为sup{n: M是n - FP -射影}，对于某FP -内射右R -模n，若Ext 1 (M, n)≠0，则ν R (M) = - 1。右ν维r。R的ν-dim(R)被定义为最小的非负整数n，使得ν R (M)≥n意味着ν R (M)对任意右R -模M =∞。如果n不存在，则设r。ν-dim(R) =∞。本文的目的是研究n - FP -射影模和环的ν维数。#由A. Facchini传达。
ABSTRACT Let R be a ring and M a right R -module. M is called n - FP -projective if Ext 1 ( M , N ) = 0 for any right R -module N of FP -injective dimension ≤ n , where n is a nonnegative integer or n = ∞. ν R ( M ) is defined as sup{ n : M is n - FP -projective} and ν R ( M ) = − 1 if Ext 1 ( M , N ) ≠ 0 for some FP -injective right R -module N . The right ν-dimension r .ν-dim( R ) of R is defined to be the least nonnegative integer n such that ν R ( M ) ≥ n implies ν R ( M ) = ∞ for any right R -module M . If no such n exists, set r .ν-dim( R ) = ∞. The aim of this paper is to investigate n - FP -projective modules and the ν-dimension of rings. #Communicated by A. Facchini.