TITLE:
A Generalization of (F,A) - Gorenstein Flat Modules
AUTHORS:
Guoqing Xu, Xi Tang
KEYWORDS:
-Gorenstein Flat Modules, Generalized -Complete Flat Resolution, Generalized -Gorenstein Flat Modules
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.4,
April
17,
2025
ABSTRACT: Inspired by Bouchiba’s work on generalized Gorenstein flat modules, we introduce the generalized
(
ℱ,A
)
-Gorenstein flat modules in this paper. By defining generalized
A
-complete flat resolution, a new measure of the dimension of generalized
(
ℱ,A
)
-Gorenstein flat modules is given. When
(
⊥
1
A,A
)
is a complete cotorsion pair,
R
is a right coherent ring and
A
contains injective right
R
-modules, it is proved that for each
M
with finite flat dimension, the generalized
(
ℱ,A
)
-Gorenstein flat dimension of
M
is equal to the
(
ℱ,A
)
-Gorenstein flat dimension of
M
.