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Everything about Direct sum of modules
Operation in abstract algebra
In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The direct sum of modules is the smallest module which contains the given modules as submodules with no "unnecessary" constraints, making it an example of a coproduct. Contrast with the direct product, which is the dual notion. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Direct sum of modulesA 5-minute orientation
- Skim a recent paper: On modules and rings having large absolute direct summandsInfluential work since 2022
- Pick up a classic book: Model Theory of Modules, Algebras and CategoriesThe most-reprinted book on the subject
- Read the landmark paper: Direct-sum representations of injective modulesCited 138 times
- Go sideways: Direct sumA closely related topic
- Go sideways: Von Neumann algebraA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Direct-sum representations of injective modules
Rings for which every module is a direct sum of cyclic modules
Direct sum decompositions of modules, semilocal endomorphism rings, and Krull monoids
Monoids of modules and arithmetic of direct-sum decompositions
Direct-sum decompositions of modules with semilocal endomorphism rings
Direct sum properties of quasi-injective modules
Direct-sum decompositions of modules with semilocal endomorphism rings
When every projective module is a direct sum of finitely generated modules
🆕 Influential since 2022
On modules and rings having large absolute direct summands
On the direct sum of dual-square-free modules
The automorphisms having the extension property in a category of a finite direct sum of cyclic modules
Essentially Quasi-Injective Modules and Their Direct Sums
Imbeddedness and direct sum of uniserial modules
📚 Books worth reading
- 📕Model Theory of Modules, Algebras and CategoriesAlberto Facchini, Lorna Gregory · 2019
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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