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.
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Supported by National Natural Science Foundation of China (Grant No. 10571152)
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Lü, J.F. On modules with d-Koszul-type submodules. Acta. Math. Sin.-English Ser. 25, 1015–1030 (2009). https://doi.org/10.1007/s10114-009-6554-8
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DOI: https://doi.org/10.1007/s10114-009-6554-8