What is a Subring? | Abstract Algebra Explained 🎓 [Old but Clear] скачать в хорошем качестве

What is a Subring? | Abstract Algebra Explained 🎓 [Old but Clear]

📌 Note: This is one of my **older videos**, and it explains a fundamental concept in Abstract Algebra – the definition and criterion of a **subring**. Despite being an older recording, the explanation is still *clear, structured, and helpful* for university students studying algebra or preparing for exams. 🎓 --- 📘 *Definition:* A subring *S* of a ring *R* is a subset of *R* that is itself a ring under the same operations. Equivalently: *Subring Criterion:* A non-empty subset *S* of *R* is a subring if:   for all *a, b ∈ S**, it follows that **a - b ∈ S* and *ab ∈ S* 👉 So *S* is closed under subtraction and multiplication. --- ✅ Let me know if you'd like a modern version of this explanation — or if you'd like me to cover more Abstract Algebra topics! 🧠 For more math videos (old and new), check out my channel playlists: [insert playlist link or channel link] #Math #AbstractAlgebra #Subring #RingTheory #UniversityMath #MathExplained #ClassicMath #OldButGold