### Abstract

The theory of groups, rings and modules is developed to a great depth. Group theory results include Zassenhaus's theorem and the Jordan-Hoelder theorem. The ring theory development includes ideals, quotient rings and the Chinese remainder theorem. The module development includes the Nakayama lemma, exact sequences and Tensor products.

### License

BSD License

### Topics

- Mathematics/Algebra

### Session Group-Ring-Module

- Algebra1
- Algebra2
- Algebra3
- Algebra4
- Algebra5
- Algebra6
- Algebra7
- Algebra8
- Algebra9

### Used by

- Fundamental Properties of Valuation Theory and Hensel’s Lemma

## Cite

×

Group-Ring-Module-AFP

    @article{Group-Ring-Module-AFP,
      author  = {Hidetsune Kobayashi and L. Chen and H. Murao},
      title   = {Groups, Rings and Modules},
      journal = {Archive of Formal Proofs},
      month   = {May},
      year    = {2004},
      note    = {\url{https://isa-afp.org/entries/Group-Ring-Module.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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