Everything about Injective module
Mathematical object in abstract algebra
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 with the Z-module Q of all rational numbers. Specifically, if Q is a submodule of some other module, then it is already a direct summand of that module; also, given a submodule of a module Y, any module homomorphism from this submodule to Q can be extended to a homomorphism from all of Y to Q. This concept is dual to that of projective modules. Injective modules were introduced in and are discussed in some detail in the textbook. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Injective moduleA 5-minute orientation
- Skim a recent paper: S-injective modulesInfluential work since 2022
- Pick up a classic book: Injective Modules and Injective Quotient RingsThe most-reprinted book on the subject
- Read the landmark paper: Algebras for which every indecomposable right module is invariant in its injective envelopeCited 46 times
- Go sideways: Module (mathematics)A closely related topic
- Go sideways: Associated primeA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Algebras for which every indecomposable right module is invariant in its injective envelope
Rings whose quasi-injective modules are injective
A Module is Flat if and Only if its Character Module is Injective
Commutative rings for which every continuous module is quasi-injective
∑-injective modules
Direct sums of m-injective modules and module classes
Closed submodules of free modules over the endomorphism ring of a quasi-injective module
On the ring of endomorphisms of an indecomposable injective module over a Prüfer ring
🆕 Influential since 2022
📚 Books worth reading
Injective Modules and Injective Quotient RingsCarl Faith · 2019
Continuous and discrete modulesSaad H. Mohamed · 1990
Lecture Notes on Local RingsBirger Iversen · 2014- 📕On selfinjective algebras of finite representation typeJosef Waschbüsch · 1983
Pseudofunctors on modules with zero dimensional supportI-Chiau Huang · 1995
Extending modulesViet Dung Nguyen · 1994
Injective modulesD. W. Sharpe · 1972
The Spectrum of a Module Category (Memoirs of the American Mathematical Society)Henning Krause · 2001
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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