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Everything about Flat module
Algebraic structure in ring theory
In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion-free modules. Formally, a module M over a ring R is flat if taking the tensor product over R with M preserves exact sequences. A module is faithfully flat if taking the tensor product with a sequence produces an exact sequence if and only if the original sequence is exact. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Flat moduleA 5-minute orientation
- Skim a recent paper: The Analysis of the Loading and the Strength of the FLAT RACK Removable Module with Viscoelastic Bonds in the FittingsInfluential work since 2022
- Pick up a classic book: Cohen-Macaulay representationsThe most-reprinted book on the subject
- Read the landmark paper: Passive cooling of standalone flat PV module with cotton wick structuresCited 285 times
- Go sideways: Projective moduleA closely related topic
- Go sideways: Glossary of commutative algebraA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Passive cooling of standalone flat PV module with cotton wick structures
Mathematical model of flat sheet membrane modules for FO process: Plate-and-frame module and spiral-wound module
Climate specific thermomechanical fatigue of flat plate photovoltaic module solder joints
Quantum homogeneous spaces with faithfully flat module structures
Fabrication and characterization of a flat-plate static-concentrator photovoltaic module
A Module is Flat if and Only if its Character Module is Injective
Spherical cap bubbles in a flat sheet nanofiltration module: experiments and numerical simulation
Lithium solvent extraction by a novel multiframe flat membrane contactor module
🆕 Influential since 2022
The Analysis of the Loading and the Strength of the FLAT RACK Removable Module with Viscoelastic Bonds in the Fittings
A dumbbell-shaped 3D flat plate pulsating heat pipe module augmented by capillarity gradient for high-power server CPU onsite cooling
Sunflower solar tree vs. flat PV module: A comprehensive analysis of performance, efficiency, and land savings in urban solar integration
Thermal characteristics of a flat plate pulsating heat pipe module for onsite cooling of high power server CPUs
Recovery of dissolved methane through a flat sheet module with PDMS, PP, and PVDF membranes
📚 Books worth reading
- 📕Cohen-Macaulay representationsGraham J. Leuschke · 2012
- 📕Model Theory of Modules, Algebras and CategoriesAlberto Facchini, Lorna Gregory · 2019
- 📕Separable AlgebrasTimothy J. Ford · 2017
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Projective module In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over…
- Glossary of commutative algebra This is a glossary of commutative algebra. See also list of algebraic geometry topics, glossary of classical algebraic geometry, glossary of algebraic…
- Commutative ring In mathematics, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative…
- Injective module In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties…
- Noetherian ring In mathematics, a Noetherian ring is a ring that satisfies the ascending chain condition on left and right ideals. If the chain condition is satisfied…
- Glossary of module theory Module theory is the branch of mathematics in which modules are studied. This is a glossary of some terms of the subject. See also: Glossary of linear…
- Glossary of ring theory Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This…
- Homological conjectures in commutative algebra In mathematics, homological conjectures have been a focus of research activity in commutative algebra since the early 1960s. They concern a number of interrelat…