S-FP-Projective Modules and Dimensions

Let R be a ring and let S be a multiplicative subset of R. An R-module M is said to be a u-S-absolutely pure module if ExtR1N,M is u-S-torsion for any finitely presented R-module N. This paper introduces and studies the notion of S-FP-projective modules, which extends the classical notion of FP-proj...

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2023, Vol.2023, p.1-10
Main Authors: Assaad, Refat Abdelmawla Khaled, Zhang, Xlaolei, Kim, Hwankoo
Format: Article
Language:English
Subjects:
Mathematics
Modules
Rings (mathematics)
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Summary:Let R be a ring and let S be a multiplicative subset of R. An R-module M is said to be a u-S-absolutely pure module if ExtR1N,M is u-S-torsion for any finitely presented R-module N. This paper introduces and studies the notion of S-FP-projective modules, which extends the classical notion of FP-projective modules. An R-module M is called an S-FP-projective module if ExtR1M,N=0 for any u-S-absolutely pure R-module N. We also introduce the S-FP-projective dimension of a module and the global S-FP-projective dimension of a ring. Then, the relationship between the S-FP-projective dimension and other homological dimensions is discussed.
ISSN:2314-4629
2314-4785
DOI:10.1155/2023/7151101