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Ring Theory

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Ring Theory Courses and Certifications

Explore abstract algebra fundamentals, ring homomorphisms, and algebraic structures through university-level mathematics. Access free video lectures on YouTube from institutions like NPTEL and Harvard CMSA, plus structured courses on Swayam covering ring theory applications in physics and cryptography.

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NPTEL; IIT Kanpur
Modern Algebra

Explore fundamental concepts and advanced topics in modern algebra through a comprehensive series of lectures by Prof. Manindra Agrawal, covering key principles and applications.
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- 14 hours
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Michael Penn
Abstract Algebra - Polynomial Rings

Explore polynomial rings, their properties, and key theorems, including the proof that R[x] is an integral domain when R is one.
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Michael Penn
Abstract Algebra - Ring Homomorphisms

Explore ring homomorphisms in abstract algebra, including definitions, examples, and key properties like multiplicative behavior and kernels.
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Abstract Algebra - Units and Zero Divisors of a Ring

Explore units and zero divisors in Zn and 2x2 real matrices, classifying elements and proving key properties in abstract algebra.
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Institut des Hautes Etudes Scientifiques (IHES)
Combinatorics and Arithmetic for Physics - Special Days 2022

Explore advanced discrete mathematics and number theory applications in theoretical physics, covering renormalization, combinatorial structures, and computational methods.
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ICTP Mathematics
Abstract Algebra

Master fundamental algebraic structures including groups, rings, and fields through comprehensive lectures by Lothar Göttsche at ICTP Mathematics.
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Commutative Algebra - Primary Decomposition

Explore primary decomposition in commutative algebra, generalizing prime factorization from integers and polynomials to arbitrary commutative rings.
- YouTube
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Commutative Algebra - Primary Decomposition 2

Delve into advanced primary decomposition theory and explore noetherianity concepts in this Oxford 3rd year mathematics lecture on commutative algebra fundamentals.
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Simons Institute
Signatures, Commitments, Zero-Knowledge, and Applications

Explore lattice-based cryptography, focusing on polynomial rings, homomorphic encryption, and zero-knowledge proofs. Learn about theoretical foundations and practical applications in modern cryptographic systems.
- YouTube
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Joint Mathematics Meetings
An Invitation to Noncommutative Algebra

Explore noncommutative algebra through symmetry, representation theory, and uncertainty principles. Discover finite and infinite dimensional solutions, formal deformations, and category theory applications.
- YouTube
- 53 minutes
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- Conference Talk
ICTP Mathematics
Hochschild (co)homology and Geometric Regularity - Andrea Solotar

Explore Hochschild (co)homology's role in geometric regularity for associative algebras. Discover its applications in commutative and non-commutative settings, and its significance in algebraic geometry.
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ICTP Mathematics
Algebraic Geometry - Lecture 3

Explore advanced concepts in algebraic geometry, focusing on complex mathematical theories and their applications in modern mathematics and theoretical physics.
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Michael Penn
A Commutative Vertex Algebra

Explore the universal commutative vertex algebra with one generator, demonstrating how to give a polynomial ring vertex algebra structure through an in-depth mathematical analysis.
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Michael Penn
The Vector Spaces for Vertex Algebras

Explore key vector spaces for vertex algebras: polynomial rings, exterior algebras with infinite variables, and universal enveloping algebra of the Virasoro Lie algebra. Gain essential understanding for advanced algebraic studies.
- YouTube
- 21 minutes
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- Free Video
Michael Penn
Abstract Algebra - Properties and Examples of Ring Homomorphisms

Explore ring homomorphisms' properties and examples, including proofs and comparisons of isomorphic groups versus rings in abstract algebra.
- YouTube
- 24 minutes
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