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Properties of Cosets (contd...), Lagrange's Theorem, Normal Subgroup, Qotient Group, Group Homomorphism, Group Automorphism, Group Isomorphism, and related Topics.
Introduction, n-ary operation, Algeraic System, Binary Operations, Semi-Group, Residue Class Modulo n, Identity, Monoid, and other topics.
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 (contd...), Lagrange's Theorem, Normal Subgroup, Qotient Group, Group Homomorphism, Group Automorphism, Group Isomorphism, and other topics.
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 Kernel, Coding Theory, Weight of a code, Distance between codewords, Properties of distance function, and other topics.
Generator matrix, Paritycheck matrix, Group Code, Decoding a group code, and other topics.
Ring of Polynomials, Root, Ring of Polynomial modulo p(x), Ideal in a Ring, Cyclic Code, and other topics.
Functions, Types of relations (1:1 etc.), Domain, codomain, Range, Identity Function, Identical Function, Surjective / Onto Function, Injective Function, Composite Function, and other topics.