Despite the fact that not all simple modules have a simple submodule, every simple module is generated by one element. Meanwhile, the idea of simple modules is particularly connected in the ring theory field of mathematics. In group theory, simple modules are analogous to simple groups. They also create building blocks for the modules of finite length.
Modular structure
Algebraic structure
Structural abstract
Simple module
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Slopes
Modules
Vector spaces
Lattice
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Ring theory
Group theory
Category theory
Abstract theory
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1
2
3
4
5
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Semi simple
Simple
Torsional
Zero
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Indecomposable
Noetherain
Torsion
Simple
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Noetherain
Indecompossable
Decomposable
Torsion
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Projective
Simple
Cyclic
Noetherain
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Noetherain
Torsionless
Torsion-free
Reducible
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