![Axioms | Free Full-Text | Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems Axioms | Free Full-Text | Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems](https://pub.mdpi-res.com/axioms/axioms-12-00341/article_deploy/html/images/axioms-12-00341-g003.png?1680247688)
Axioms | Free Full-Text | Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems
1) [20 points] If u is a unit in a commutative ring, prove that it's inverse is unique: if ua = 1 and ub = 1, then a = b. Just
![abstract algebra - Why is commutativity optional in multiplication for rings? - Mathematics Stack Exchange abstract algebra - Why is commutativity optional in multiplication for rings? - Mathematics Stack Exchange](https://i.stack.imgur.com/UyIXV.jpg)
abstract algebra - Why is commutativity optional in multiplication for rings? - Mathematics Stack Exchange
![Example Solutions and Answers for examples - Example Sheet 1 - Rings and Subrings LetRbe the set of - Studocu Example Solutions and Answers for examples - Example Sheet 1 - Rings and Subrings LetRbe the set of - Studocu](https://d20ohkaloyme4g.cloudfront.net/img/document_thumbnails/375c9b14cfa2e8db5a58a6a986479d3a/thumb_1200_1697.png)