# Algebraic Structures - Groups and Rings

##### Video Lessons & Revision Notes

Algebraic System - Basic Concepts, Semi Group, Identity Element and Monoids
1. Algebraic System - Basic Concepts, Semi Group, Identity Element and Monoids
In this 50 mins Video Lesson
Introduction, n-ary operation, Algeraic System, Binary Operations, Semi-Group, Residue Class Modulo n, Identity, Monoid, and other topics.
Inverse, Groups, Abelian Group, Cyclic Group and Cosets
2. Inverse, Groups, Abelian Group, Cyclic Group and Cosets
In this 53 mins Video Lesson
Inverse of an Element, Group, Abelian Group, Order of a Group, Order of An element, Cyclic Group, Product Group, Properties of a Group, Sub-Group, Cosets, Properties of a Coset, and other topics.
Properties of Cosets, Normal Sub Group, Homomorphism, Automorphism, Isomorphism
3. Properties of Cosets, Normal Sub Group, Homomorphism, Automorphism, Isomorphism
In this 47 mins Video Lesson
Properties of Cosets (contd...), Lagrange's Theorem, Normal Subgroup, Qotient Group, Group Homomorphism, Group Automorphism, Group Isomorphism, and other topics.
Ring, Integral Domain and Fields
4. Ring, Integral Domain and Fields
In this 52 mins Video Lesson
Rings, Commutative Ring, Ring with no proper Divisors of 0, Ring with a unity, Unit of a Ring, Integral Domain, Field, Properties of Rings, Example, and other topics.
Ring Homomorphism and Coding Theory
5. Ring Homomorphism and Coding Theory
In this 34 mins Video Lesson
Ring Homomorphism and Kernel, Coding Theory, Weight of a code, Distance between codewords, Properties of distance function, and other topics.
Coding Theory (Contd.), Generator, Parity Check Matrix and Group Code
6. Coding Theory (Contd.), Generator, Parity Check Matrix and Group Code
In this 41 mins Video Lesson
Generator matrix, Paritycheck matrix, Group Code, Decoding a group code, and other topics.
Ring of Polynomial and Cyclic Code
7. Ring of Polynomial and Cyclic Code
In this 29 mins Video Lesson
Ring of Polynomials, Root, Ring of Polynomial modulo p(x), Ideal in a Ring, Cyclic Code, and other topics.

### Revision Notes

Algebraic Systems, Groups, Semi Groups, Monoid, Subgroups, Permutation Groups, Codes and Group codes, Isomorphism and Automorphisms, Homomorphism and Normal Subgroups, Ring, Integral Domain, Field, Ring Homomorphism, Polynomial Rings and Cyclic Code