Mathlib Phrasebook

17. Ring extensions🔗

This page explains how to write a tower of ring extensions in Mathlib. We assume that you have read Mathematics in Lean chapter 9 on Groups and Rings. We will explain how Mathlib represents the following sentence: "Let R, S and T be commutative rings, such that R is included in S and S is included in T." Although we focus on commutative rings for simplicity, everything holds unless mentioned otherwise for semirings and fields. See The non-unital, non-associative case for info on generalizing the assumptions further.

  1. 17.1. Algebras
  2. 17.2. Towers of extensions
  3. 17.3. Subrings
  4. 17.4. The non-unital, non-associative case