Let R be a ring and let S be a multiplicative subset of R. An R‐module M is said to be au‐S‐
absolutely pure module if Ext R 1 N, M is u‐S‐torsion for any finitely presented R‐module N …

Let R be a ring and let S be a multiplicative subset of R. An R-module M is said to be a uS-
absolutely pure module if Ext R 1 N, M is uS-torsion for any finitely presented R-module N …

Let R be a ring and let S be a multiplicative subset of R. An R-module M is said to be a uS-
absolutely pure module if ExtR1N, M is uS-torsion for any finitely presented R-module N …

Let R be a ring and let S be a multiplicative subset of R. An R-module M is said to be a uS-
absolutely pure module if ExtR1N, M is uS-torsion for any finitely presented R-module N …

Troughout the paper, all rings considered are commutative with identity, all modules are
unitary, and S is always a multiplicative subset of R, that is, 1∈ S and s1s2∈ S for any s1 …

Let R be a ring. An R-module M is said to be an absolutely w-pure module if and only if Ext1
R (F, M) is a GV-torsion module for any finitely presented module F. In this paper, we …