On modules with <Emphasis Type="Italic">d</Emphasis>-Koszul-type submodules |
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Authors: | Jia Feng Lü |
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Institution: | (1) College of Mathematics and Physics, Zhejiang Normal University, Jinhua, 321004, P. R. China |
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Abstract: | The so-called weakly d-Koszul-type module is introduced and it turns out that each weakly d-Koszul-type module contains a d-Koszul-type submodule. It is proved that, M ∈
ℐ
d
(A) if and only if M admits a filtration of submodules: 0 ⊂ U
0 ⊂ U
1 ⊂ ... ⊂ U
p
= M such that all U
i
/U
i−1 are d-Koszul-type modules, from which we obtain that the finitistic dimension conjecture holds in
ℐ
d
(A) in a special case. Let M ∈
∐
d
(A). It is proved that the Koszul dual ℰ(M) is Noetherian, Hopfian, of finite dimension in special cases, and ℰ(M) ∈ gr0(E(A)). In particular, we show that M ∈
ℐ
d
(A) if and only if ℰ (G(M)) ∈ gr0(E(A)), where G is the associated graded functor.
Supported by National Natural Science Foundation of China (Grant No. 10571152) |
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Keywords: | d-Koszul-type algebras and modules weakly d-Koszul-type modules |
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