Gorenstein AC-projective dimension of unbounded complexes |
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Authors: | Zhenxing Di Xiaoxiang Zhang Jianlong Chen |
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Affiliation: | 1. Department of Mathematics, Northwest Normal University, Lanzhou, Chinadizhenxing19841111@126.com;3. Department of Mathematics, Southeast University, Nanjing, China |
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Abstract: | Recently, the notion of Gorenstein AC-projective (resp., Gorenstein AC-injective) modules was introduced in [3 Bravo, D., Gillespie, J., Hovey, M. The stable module category of a general ring. http://arxiv.org/abs/1405.5768. [Google Scholar]] by which the so-called “Gorenstein AC-homological algebra” was established. Here, we define and study a notion of Gorenstein AC-projective dimension for complexes (not necessarily bounded) over associative rings, which is inspired by Veliche’s construction of defining Gorenstein projective dimension. In particular, we show that such a dimension can be closely related to the “proper” Gorenstein AC-projective resolutions of complexes induced by a complete and hereditary cotorsion pair in the category of complexes of modules. This enables us to interpret this dimension of a complex in terms of vanishing of the derived functor RHomR(?,?). As applications, some characterizations of the Gorenstein AC-projective dimension of a module are also obtained. |
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Keywords: | Cotorsion pair dimension Gorenstein AC-projective module level module |
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