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🔹 What makes a Ring more than just numbers? 🤔
Let’s explore the definition of a Ring in Abstract Algebra — a fundamental concept every undergraduate Mathematics student must know.

A Ring is a set with two operations that satisfy specific rules:

➕ Addition properties: commutativity, associativity, identity, inverse

✖️ Multiplication properties: associativity

🔄 Distributive laws: connecting addition & multiplication

After the definition, we dive into powerful examples of rings:
1️⃣ Integers (ℤ) – a ring with unity
2️⃣ Even integers (2ℤ) – a commutative ring
3️⃣ Modular integers (ℤₙ) – key in number theory & cryptography
4️⃣ Polynomial rings (ℝ[x]) – polynomials with real coefficients
5️⃣ Matrix rings (Mₙ(ℝ)) – all n×n real matrices
6️⃣ Function rings – real-valued functions with pointwise operations

🎯 By the end of this lecture, you’ll grasp the concept of rings with clarity — useful for B.Sc. Maths courses, exams, and higher studies in Algebra.

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