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Everything about Singular submodule
In the branches of abstract algebra known as ring theory and module theory, each right (resp. left) R-module M has a singular submodule consisting of elements whose annihilators are essential right (resp. left) ideals in R. In set notation it is usually denoted as. For general rings, is a good generalization of the torsion submodule tors(M) which is most often defined for domains. In the case that R is a commutative domain,. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Singular submoduleA 5-minute orientation
- Skim a recent paper: On Total Graphs Related to Cosingular SubmoduleInfluential work since 2022
- Read the landmark paper: The singular submodule splits offCited 17 times
- Go sideways: Semisimple moduleA closely related topic
- Go sideways: Uniform moduleA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
The singular submodule splits off
Singular Submodule and Injective Hull
Quotient rings of endomorphism rings of modules with zero singular submodule
Total graph of a module with respect to singular submodule
On commutative rings over which the singular submodule is a direct summand for every module
On Modules of Singular Submodule Zero
The singular submodule of a finitely generated module splits off
Rickart modules relative to singular submodule and dual Goldie torsion theory
🆕 Influential since 2022
📚 Books worth reading
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🔗 Related topics
- Semisimple module In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module…
- Uniform module In abstract algebra, a module is called a uniform module if the intersection of any two nonzero submodules is nonzero. This is equivalent to saying that…
- Noncommutative ring In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are…
- 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…
- Quasi-Frobenius ring In mathematics, especially ring theory, the class of Frobenius rings and their generalizations are the extension of work done on Frobenius algebras. Perhaps…
- Dense submodule In abstract algebra, specifically in module theory, a dense submodule of a module is a refinement of the notion of an essential submodule. If N is a dense…
- 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…
- Finitely generated module In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called…