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Everything about Projective module
Direct summand of a free module (mathematics)
In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules over a ring, keeping some of the main properties of free modules. Various equivalent characterizations of these modules appear below. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Projective moduleA 5-minute orientation
- Skim a recent paper: When every S -flat module is (flat) projectiveInfluential work since 2022
- Pick up a classic book: Continuous and discrete modulesThe most-reprinted book on the subject
- Read the landmark paper: Gorenstein projective dimension with respect to a semidualizing moduleCited 78 times
- Go sideways: Flat moduleA closely related topic
- Go sideways: Commutative ringA closely related topic
📖 Definitions
Noun A module which is a direct summand of a free module.
🏆 Landmark papers (most cited)
Gorenstein projective dimension with respect to a semidualizing module
Rank Element of a Projective Module
Projective Module Description of the q -Monopole
When every finitely generated flat module is projective
Modules over the endomorphism ring of a finitely generated projective module
On the depth and the projective dimension of the canonical module
Divisibility of Projective Modules of Finite Chevalley Groups by the Steinberg Module
A non-projective module without self-extensions
🆕 Influential since 2022
When every S -flat module is (flat) projective
Bourbaki modules and the module of Jacobian derivations of projective hypersurfaces
Projective Indecomposable Permutation Modules
RD-projective module whose subprojectivity domain is minimal
Existence of unimodular element in a projective module over symbolic Rees algebras
📚 Books worth reading
Continuous and discrete modulesSaad H. Mohamed · 1990- 📕Micro-optic color separation technology for efficient projection displaysW. J. Gunning · 1997
General Galois GeometriesJames Hirschfeld, Joseph A. Thas · 2016
Théorèmes de Bertini et applicationsJean-Pierre Jouanolou · 1979
Ideals and realityFriedrich Ischebeck · 2005
Projective modules over Lie algebras of Cartan typeDaniel K. Nakano · 1992
Serre's Problem on Projective ModulesT.Y. Lam · 2006
K3 Projective models in scrollsTrygve Johnsen · 2004
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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