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Special precovering classes in comma categories.
- Source :
- SCIENCE CHINA Mathematics; May2022, Vol. 65 Issue 5, p933-950, 18p
- Publication Year :
- 2022
-
Abstract
- Let T be a right exact functor from an abelian category ℬ into another abelian category A . Then there exists a functor p from the product category A × ℬ to the comma category ( (T ↓ A) ). In this paper, we study the property of the extension closure of some classes of objects in ( (T ↓ A) ), the exactness of the functor p and the detailed description of orthogonal classes of a given class P (X , Y) in ( (T ↓ A) ). Moreover, we characterize when special precovering classes in abelian categories A and ℬ can induce special precovering classes in ( (T ↓ A) ). As an application, we prove that under suitable cases, the class of Gorenstein projective left Λ-modules over a triangular matrix ring Λ = ( R M 0 S ) is special precovering if and only if both the classes of Gorenstein projective left R-modules and left S-modules are special precovering. Consequently, we produce a large variety of examples of rings such that the class of Gorenstein projective modules is special precovering over them. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16747283
- Volume :
- 65
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- SCIENCE CHINA Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 156526192
- Full Text :
- https://doi.org/10.1007/s11425-020-1790-9