Module Theory

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Notes

• Modules
  • Examples of Modules
• Category of Modules
• Submodule and quotients
• Cannonical Decomposition of Module Homomorphisms
• Direct sum of Modules
  • Infinte product and coproduct of modules do not coincide
• Kernel and Cokernels in R-Mod
• R-Mod is a CCC
• Free Module
  • If R is a PID then submodules of free module over R are free
• Free Algebra
• Noetherian Modules
  • M is noetherian if for every sub-module N, N and MN are noetherian
  • If R is noetherian and M is finitely generated then M is noetherian
• Finite Type Algebra
• Left and Right Inverses of Ring Homomorphisms

Existence of Factors

• Ascending Chain Condition

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MOCs

• Ring Theory
• Category Theory
• Homology Theory

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References