ring-ideal-proof

Prove ring and ideal properties with machine-checked Lean 4 proofs.

3|Updated Feb 9, 2026

Search Tags:#mathlib #algebra #proof #ring-theory #lean-prover #ideals #quotients

Ready to run

npx skills add https://github.com/0bserver07/bourbaki --skill ring-ideal-proof

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: ring-ideal-proof
Source: https://github.com/0bserver07/bourbaki/tree/main/src/skills/ring-ideal-proof
Command: npx skills add https://github.com/0bserver07/bourbaki --skill ring-ideal-proof

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Prove properties about rings, ideals, and quotient rings with a structured, verifiable approach that ties algebraic reasoning to Lean-based formalization.

Core Features & Use Cases

Prove ideal properties, quotient ring constructions, and the relationship between primes, maximal ideals, and quotient structures.
Apply the First Isomorphism Theorem, the Correspondence Theorem, and quotient techniques to classical algebra problems.
Use Lean 4 + Mathlib to machine-check proofs and produce formal certificates for algebraic statements.

Quick Start

Provide a ring R and an ideal I, then use Lean 4 with Mathlib to verify properties of I and R/I.

Frequently Asked Questions about ring-ideal-proof

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I formalize ring theory proofs about ideals and quotient rings in Lean?▼

You formalize ring theory proofs by providing a ring R and an ideal I, then applying Lean 4 with Mathlib to machine-check properties of quotient constructions and produce formal certificates for algebraic statements.

Can I prove the First Isomorphism Theorem and Correspondence Theorem using Lean 4 and Mathlib?▼

Yes, you can apply the First Isomorphism Theorem and the Correspondence Theorem to classical algebra problems using Lean 4 with Mathlib to generate machine-checked proofs for ring homomorphisms and quotient structures.

Does this approach support proving properties of prime and maximal ideals in quotient structures?▼

Yes, proving properties of prime and maximal ideals is supported by applying quotient techniques and ring homomorphism properties to verify the relationship between these ideals and quotient ring structures.

Do I need Lean 4 and Mathlib to verify algebraic statements about ring homomorphisms?▼

Yes, Lean 4 with Mathlib is required to machine-check proofs and produce formal certificates for algebraic statements involving ring homomorphisms, ideal properties, and quotient ring constructions.

What is the best way to machine-check quotient ring constructions for classical algebra problems?▼

The best way to machine-check quotient ring constructions is using Lean 4 with Mathlib to formally verify the algebraic reasoning and generate verifiable proof certificates for ring theory theorems.

Why use Lean-based formalization instead of manual proofs for ring theory problems?▼

Lean-based formalization ties algebraic reasoning to machine-checked verification, ensuring that proofs about ideals, quotient rings, and homomorphisms are structurally sound and produce formal certificates rather than relying on manual checks.