Ring Theory Courses and Certifications

Rings and polynomials

2 ratings at OpenLearn

This free course contains an introduction to rings and polynomials. We see that polynomial rings have many properties in common with the integers; for example, we can define a division algorithm, ...

• OpenLearn
• 16 hours
• Self-Paced
• Free Certificate

IIT Kharagpur;  NPTEL

Rings and Modules

1 rating

An elementary introduction to ring and module theory, spanning ideals, factorization, structural conditions, and tensor products.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

Michael Penn

Abstract Algebra - The Division Algorithm for Polynomials

A proof of the polynomial division algorithm over a field, a foundational result in abstract algebra.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Michael Penn

Abstract Algebra - Polynomial Rings

Introduces polynomial rings through examples and proves that R[x] is an integral domain whenever R is an integral domain.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Michael Penn

Abstract Algebra - Ring Homomorphisms

Learn the definition and properties of ring homomorphisms through examples, multiplicative behavior, and kernels.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

Michael Penn

Abstract Algebra - Units and Zero Divisors of a Ring

Classifies units and zero divisors in ℤₙ and the ring of 2×2 real matrices.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

Michael Penn

How the Power Set Forms a Ring

Explore how the power set forms a ring in this mathematical demonstration, showcasing set theory principles and algebraic structures.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Michael Penn

Abstract Algebra - If D is a UFD then D[x] is a UFD

A proof that polynomial rings over unique factorization domains are themselves unique factorization domains, using content, Gauss’ lemma, and fraction fields.

• YouTube
• 26 minutes
• Self-Paced
• Free Video

Michael Penn

Abstract Algebra - The Field of Fractions of an Integral Domain

Constructs the field of fractions of an integral domain, with examples and a proof that it is the smallest containing field.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Michael Penn

Abstract Algebra - Properties and Examples of Ring Homomorphisms

Explore why 2ℤ and 3ℤ can be isomorphic as groups but not as rings through properties of ring homomorphisms.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Wolfram

Noncommutative Algebra and Its Applications

Explore Mathematica's new noncommutative algebra functionality, including polynomial transformations, Groebner bases, and computations with Weyl, Clifford, and Grassmann algebras.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Wolfram

Expanding Exponentials in Noncommutative Algebras

Explore advanced mathematical formulas for decomposing exponentials in noncommutative settings, featuring Wolfram Language implementations and applications to operator theory.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Abstract Algebra - Polynomial Rings

Explore polynomial rings through division algorithms, polynomial gcds, irreducibility, Eisenstein’s criterion, PID structure, and construction of a field of order 4.

• YouTube
• 2 hours 30 minutes
• Self-Paced
• Free Video

Abstract Algebra

Introduces abstract algebra through groups, homomorphisms, rings, fields, vector spaces, and modules, emphasizing core algebraic structures and their relationships.

• YouTube
• 3 hours 30 minutes
• Self-Paced
• Free Video

IMSC;  NPTEL

Algebra - I

Graduate-level abstract algebra develops groups, rings, modules, and their classification, culminating in finitely generated abelian groups and Jordan canonical form.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course