Flat modules and rings finitely generated as modules over their center

1996 ◽  
Vol 60 (2) ◽  
pp. 186-203 ◽  
Author(s):  
A. A. Tuganbaev
Keyword(s):  
Finitely Generated ◽  
Flat Modules

Projectivity of finitely generated flat modules over semilocal rings

1985 ◽  
Vol 37 (2) ◽  
pp. 85-90
Author(s):  
I. I. Sakhaev
Keyword(s):  
Finitely Generated ◽  
Flat Modules

Finitely Generated Flat Modules and a Characterization of Semiperfect Rings

2003 ◽  
Vol 31 (9) ◽  
pp. 4195-4214 ◽  
Author(s):  
Alberto Facchini ◽  
Dolors Herbera ◽  
Iskhak Sakhajev
Keyword(s):  
Finitely Generated ◽  
Flat Modules

scholarly journals Flat modules and lifting of finitely generated projective modules

2005 ◽  
Vol 220 (1) ◽  
pp. 49-68 ◽  
Author(s):  
Alberto Facchini ◽  
Dolors Herbera ◽  
Iskhak Sakhajev
Keyword(s):  
Projective Modules ◽  
Finitely Generated ◽  
Flat Modules

scholarly journals On finitely generated flat modules

1969 ◽  
Vol 138 ◽  
pp. 505-505 ◽  
Author(s):  
Wolmer V. Vasconcelos
Keyword(s):  
Finitely Generated ◽  
Flat Modules

scholarly journals On Finitely Generated Flat Modules.

1970 ◽  
Vol 26 ◽  
pp. 233 ◽  
Author(s):  
S. Jondrup
Keyword(s):  
Finitely Generated ◽  
Flat Modules

Almost étale coverings

2017 ◽  
Author(s):  
Ahmed Abbes ◽  
Michel Gros ◽  
Takeshi Tsuji
Keyword(s):  
Galois Cohomology ◽  
Hodge Theory ◽  
Group Cohomology ◽  
Arithmetic Geometry ◽  
Projective Modules ◽  
Historical Overview ◽  
Finitely Generated ◽  
Smooth Variety ◽  
Flat Modules ◽  
Étale Cohomology

This chapter explains Faltings' theory of almost étale extensions, a tool that has become essential in many questions in arithmetic geometry, even beyond p-adic Hodge theory. It begins with a brief historical overview of almost étale extensions, noting how Faltings developed the “almost purity theorem” and proved the Hodge–Tate decomposition of the étale cohomology of a proper smooth variety. The chapter proceeds by discussing almost isomorphisms, almost finitely generated projective modules, trace, rank and determinant, almost flat modules and almost faithfully flat modules, almost étale coverings, almost faithfully flat descent, and liftings. Finally, it describes group cohomology of discrete A–G-modules and Galois cohomology.

J-COHERENT RINGS

2009 ◽  
Vol 08 (02) ◽  
pp. 139-155 ◽  
Author(s):  
NANQING DING ◽  
YUANLIN LI ◽  
LIXIN MAO
Keyword(s):  
Jacobson Radical ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finitely Generated ◽  
Flat Modules ◽  
Coherent Ring ◽  
Necessary And Sufficient ◽  
Coherent Rings ◽  
Finitely Presented

Let R be a ring. Recall that a left R-module M is coherent if every finitely generated submodule of M is finitely presented. R is a left coherent ring if the left R-module RR is coherent. In this paper, we say that R is left J-coherent if its Jacobson radical J(R) is a coherent left R-module. J-injective and J-flat modules are introduced to investigate J-coherent rings. Necessary and sufficient conditions for R to be left J-coherent are given. It is shown that there are many similarities between coherent and J-coherent rings. J-injective and J-flat dimensions are also studied.

scholarly journals On Finitely Generated Flat Modules II.

1970 ◽  
Vol 27 ◽  
pp. 105 ◽  
Author(s):  
S. Jondrup
Keyword(s):  
Finitely Generated ◽  
Flat Modules

scholarly journals On Finitely Generated Flat Modules III.

1971 ◽  
Vol 29 ◽  
pp. 206
Author(s):  
S. Jondrup
Keyword(s):  
Finitely Generated ◽  
Flat Modules

Subprojectivity domains of pure-projective modules

2019 ◽  
Vol 19 (05) ◽  
pp. 2050091
Author(s):  
Yılmaz Durğun
Keyword(s):  
Noetherian Ring ◽  
Projective Module ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Projective Modules ◽  
Finitely Generated ◽  
Flat Modules ◽  
Necessary And Sufficient

In a recent paper, Holston et al. have defined a module [Formula: see text] to be [Formula: see text]-subprojective if for every epimorphism [Formula: see text] and homomorphism [Formula: see text], there exists a homomorphism [Formula: see text] such that [Formula: see text]. Clearly, every module is subprojective relative to any projective module. For a module [Formula: see text], the subprojectivity domain of [Formula: see text] is defined to be the collection of all modules [Formula: see text] such that [Formula: see text] is [Formula: see text]-subprojective. We consider, for every pure-projective module [Formula: see text], the subprojective domain of [Formula: see text]. We show that the flat modules are the only ones sharing the distinction of being in every single subprojectivity domain of pure-projective modules. Pure-projective modules whose subprojectivity domain is as small as possible will be called pure-projective indigent (pp-indigent). Properties of subprojectivity domains of pure-projective modules and of pp-indigent modules are studied. For various classes of modules (such as simple, cyclic, finitely generated and singular), necessary and sufficient conditions for the existence of pp-indigent modules of those types are studied. We characterize the structure of a Noetherian ring over which every (simple, cyclic, finitely generated) pure-projective module is projective or pp-indigent. Furthermore, finitely generated pp-indigent modules on commutative Noetherian hereditary rings are characterized.

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