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| Relative T -Injective Modules and Relative T -Flat Modules |
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Citation： |
Mohammad Javad NIKMEHR,Farzad SHAVEISI.Relative T -Injective Modules and Relative T -Flat Modules[J].Chinese Annals of Mathematics B,2011,32(4):497~506 |
| Page view： 1697
Net amount： 1240 |
Authors： |
Mohammad Javad NIKMEHR; Farzad SHAVEISI; |
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| Abstract： |
Let $T$ be a Wakamatsu tilting module. A module $M$ is called
$(n,T)$-copure injective (resp. $(n,T)$-copure flat) if
${\mathcal{E}}_{T}^{1}(N,M)=0$ (resp. ${\Gamma}_{1}^{T}(N,M)=0$)
for any module $N$ with $T$-injective dimension at most $n$ (see Definition \ref{2.2}).
In this paper, it is shown that $M$ is $(n,T)$-copure injective if and only if $M$
is the kernel of an ${\mathcal{I}}_n(T)$-precover $f:A\rightarrow B$ with $A\in{\rm Prod}\,T$.
Also, some results on ${\rm Prod}\,T$-syzygies are presented. For
instance, it is shown that every $n{\rm th}$ ${\rm Prod}\,T$-syzygy
of every module, generated by $T$, is $(n,T)$-copure injective. |
Keywords： |
Wakamatsu tilting module, (n, T )-Copure injective module, (n, T )-
Copure flat module, T-Projective dimension, T-Injective dimension |
Classification： |
13D05, 13D07, 13D99 |
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