### Abstract

The focus of this case study is re-use in abstract algebra. It contains locale-based formalisations of selected parts of set, group and ring theory from Jacobson's Basic Algebra leading to the respective fundamental homomorphism theorems. The study is not intended as a library base for abstract algebra. It rather explores an approach towards abstract algebra in Isabelle.

### License

BSD License

### Topics

- Mathematics/Algebra

### Session Jacobson_Basic_Algebra

- Set_Theory
- Group_Theory
- Ring_Theory

### Used by

- Kneser’s Theorem and the Cauchy–Davenport Theorem
- Khovanskii's Theorem
- The Plünnecke-Ruzsa Inequality
- Grothendieck’s Schemes in Algebraic Geometry

## Cite

×

Jacobson_Basic_Algebra-AFP

    @article{Jacobson_Basic_Algebra-AFP,
      author  = {Clemens Ballarin},
      title   = {A Case Study in Basic Algebra},
      journal = {Archive of Formal Proofs},
      month   = {August},
      year    = {2019},
      note    = {\url{https://isa-afp.org/entries/Jacobson_Basic_Algebra.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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## Download

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Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
- Feb 23, 2021 : Isabelle2021
- Apr 18, 2020 : Isabelle2020
- Sep 1, 2019 : Isabelle2019