Relative Weak Injective and Weak Flat Modules with Respect to a Semidualizing Module

Gorenstein Flat Complexes with Respect to a Semidualizing Module

Algebra Colloquium ◽

10.1142/s1005386715000231 ◽

2015 ◽

Vol 22 (02) ◽

pp. 259-270

Author(s):

Li Liang ◽

Chunhua Yang

Keyword(s):

Noetherian Ring ◽

Commutative Noetherian Ring ◽

Semidualizing Module ◽

Flat Modules ◽

Gorenstein Flat

In this paper, we introduce and study G C-flat complexes over a commutative Noetherian ring, where C is a semidualizing module. We prove that G C-flat complexes are actually the complexes of G C-flat modules. This complements a result of Yang and Liang. As an application, we get that every complex has a [Formula: see text]-cover, where [Formula: see text] is the class of G C-flat complexes. We also give a characterization of complexes of modules in [Formula: see text] that are defined by Sather-Wagstaff, Sharif and White.

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SG_C-Projective, Injective and Flat modules

Journal of the Indonesian Mathematical Society ◽

10.22342/jims.25.2.754.108-120 ◽

2019 ◽

Vol 25 (2) ◽

pp. 108-120

Author(s):

Parimala M ◽

Udhayakumar Ramalingam

Keyword(s):

Semidualizing Module ◽

Flat Modules

In this paper we introduce the concepts of $SG_C$-projective, injective and flat modules, where $C$ is a semidualizing module and we discuss some connections among $SG_C$-projective, injective and flat modules.

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Projectivity of finitely generated flat modules over semilocal rings

Mathematical Notes ◽

10.1007/bf01156749 ◽

1985 ◽

Vol 37 (2) ◽

pp. 85-90

Author(s):

I. I. Sakhaev

Keyword(s):

Finitely Generated ◽

Flat Modules

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Noncommutative G-semihereditary rings

Journal of Algebra and Its Applications ◽

10.1142/s0219498818500147 ◽

2018 ◽

Vol 17 (01) ◽

pp. 1850014 ◽

Cited By ~ 2

Author(s):

Jian Wang ◽

Yunxia Li ◽

Jiangsheng Hu

Keyword(s):

Associative Ring ◽

Sufficient Condition ◽

Projective Modules ◽

The Third ◽

Flat Modules ◽

Gorenstein Projective Modules ◽

Direct Limits ◽

Gorenstein Flat ◽

Finitely Presented ◽

Semihereditary Rings

In this paper, we introduce and study left (right) [Formula: see text]-semihereditary rings over any associative ring, and these rings are exactly [Formula: see text]-semihereditary rings defined by Mahdou and Tamekkante provided that [Formula: see text] is a commutative ring. Some new characterizations of left [Formula: see text]-semihereditary rings are given. Applications go in three directions. The first is to give a sufficient condition when a finitely presented right [Formula: see text]-module is Gorenstein flat if and only if it is Gorenstein projective provided that [Formula: see text] is left coherent. The second is to investigate the relationships between Gorenstein flat modules and direct limits of finitely presented Gorenstein projective modules. The third is to obtain some new characterizations of semihereditary rings, [Formula: see text]-[Formula: see text] rings and [Formula: see text] rings.

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