Dimension of complexes related to special Gorenstein projective precovers(II). Issue 3 (4th March 2023)

• Record Type: Journal Article
• Authors: Liu, Zhongkui; Pengju, Ma
• Is Part Of: Communications in algebra. Volume 51:Issue 3(2023)
• Page Start: 1308
• Page End: 1319
• Publication Date: 2023-03-04
• Subjects: Complete Gorenstein projective resolution -- complete preenvelope-precover resolution -- Gppd -- relative cohomology group -- special Gorenstein projective precover; 16E10 -- 16E05 -- 16E30; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2022.2134408
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let R be a ring and X a complex of R -modules. We give some characterizations of the dimension of X related to special Gorenstein projective precovers. Let R be a ring such that ( G P, G P ⊥ ) forms a cotorsion pair cogenerated by a set, where G P denotes the category consisting of all Gorenstein projective R -modules. Then the dimension related to special Gorenstein projective precovers Gppd ( X ) is equal to the infimum of the set { n ∈ Z | there exists a complete Gorenstein projective resolution of X T → σ G → X such that σi is bijective for each i ≥ n } . Forthmore, if Gppd ( X ) is finite and n an integer then Gppd ( X ) ≤ n if and only if Ext G P i ( X, Q ) = 0 for any i > n and any projective R -module Q, where Ext G P i ( −, − ) is the relative cohomology functor.