Coherent rings and Gorenstein flat character modules

2020 ◽  
pp. 1-10
Author(s):  
Yanjiong Yang ◽  
Xiaoguang Yan ◽  
Guocheng Dai
Keyword(s):  
Coherent Rings ◽  
Gorenstein Flat

scholarly journals STRONGLY GORENSTEIN FLAT MODULES

2009 ◽  
Vol 86 (3) ◽  
pp. 323-338 ◽  
Author(s):  
NANQING DING ◽  
YUANLIN LI ◽  
LIXIN MAO
Keyword(s):  
Exact Sequence ◽  
Projective Modules ◽  
Flat Dimension ◽  
Flat Modules ◽  
Coherent Rings ◽  
Gorenstein Flat ◽  
Strongly Gorenstein Flat Modules

AbstractIn this paper, strongly Gorenstein flat modules are introduced and investigated. An R-module M is called strongly Gorenstein flat if there is an exact sequence ⋯→P1→P0→P0→P1→⋯ of projective R-modules with M=ker (P0→P1) such that Hom(−,F) leaves the sequence exact whenever F is a flat R-module. Several well-known classes of rings are characterized in terms of strongly Gorenstein flat modules. Some examples are given to show that strongly Gorenstein flat modules over coherent rings lie strictly between projective modules and Gorenstein flat modules. The strongly Gorenstein flat dimension and the existence of strongly Gorenstein flat precovers and pre-envelopes are also studied.

scholarly journals Cartan-Eilenberg Gorenstein Flat Complexes

2014 ◽  
Vol 114 (1) ◽  
pp. 5 ◽  
Author(s):  
Gang Yang ◽  
Li Liang
Keyword(s):  
Coherent Ring ◽  
Coherent Rings ◽  
Flat Cover ◽  
Gorenstein Flat

In this paper, we study Cartan-Eilenberg Gorenstein flat complexes. We show that over coherent rings a Cartan-Eilenberg Gorenstein flat complex can be gotten by a so-called complete Cartan-Eilenberg flat resolution. We argue that over a coherent ring every complex has a Cartan-Eilenberg Gorenstein flat cover.

GORENSTEIN FP-INJECTIVE AND GORENSTEIN FLAT MODULES

2008 ◽  
Vol 07 (04) ◽  
pp. 491-506 ◽  
Author(s):  
LIXIN MAO ◽  
NANQING DING
Keyword(s):  
Exact Sequence ◽  
Injective Modules ◽  
Flat Modules ◽  
Coherent Rings ◽  
Gorenstein Flat

In this paper, Gorenstein FP-injective modules are introduced and studied. An R-module M is called Gorenstein FP-injective if there is an exact sequence ⋯ → E1 → E0 → E0 → E1 → ⋯ of injective R-modules with M = ker (E0 → E1) and such that Hom (E, -) leaves the sequence exact whenever E is an FP-injective R-module. Some properties of Gorenstein FP-injective and Gorenstein flat modules over coherent rings are obtained. Several known results are extended.

scholarly journals A Note on Gorenstein Flat Dimension

2011 ◽  
Vol 18 (01) ◽  
pp. 155-161 ◽  
Author(s):  
Driss Bennis
Keyword(s):  
Associative Ring ◽  
Projective Dimension ◽  
Flat Dimension ◽  
Coherent Rings ◽  
Gorenstein Flat

Unlike the Gorenstein projective and injective dimensions, the majority of results on the Gorenstein flat dimension have been established only over Noetherian (or coherent) rings. Naturally, one would like to generalize these results to any associative ring. In this direction, we show that the Gorenstein flat dimension is a refinement of the classical flat dimension over any ring; and we investigate the relations between the Gorenstein projective dimension and the Gorenstein flat dimension.

scholarly journals Gorenstein flat representations of left rooted quivers

2021 ◽  
Author(s):  
Zhenxing Di ◽  
Sergio Estrada ◽  
Li Liang ◽  
Sinem Odabaşı
Keyword(s):  
Gorenstein Flat

scholarly journals On Gorenstein Flat Preenvelopes of Complexes

2013 ◽  
Vol 129 ◽  
pp. 171-187 ◽  
Author(s):  
Gang Yang ◽  
Zhongkui Liu ◽  
Li Liang
Keyword(s):  
Gorenstein Flat

Noncommutative G-semihereditary rings

2018 ◽  
Vol 17 (01) ◽  
pp. 1850014 ◽  
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.

Notes on Gorenstein Flat Modules

2018 ◽  
Vol 45 (2) ◽  
pp. 337-344
Author(s):  
Yanjiong Yang ◽  
Xiaoguang Yan
Keyword(s):  
Flat Modules ◽  
Gorenstein Flat
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