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Syllabus 📚
Calendar 📅
Homeworks ✏️
Notes 📓
Chapter 1
Division Algorithm
Proof of the Division Algorithm
Divisibility
Euclidean Algorithm
Prime Numbers
Fundamental Theorem of Arithmetic
Chapter 2
Congruence in the set of integers
The Set of Congruence Classes
Operations on Congruence Classes
Special Features of Z_p
Chapter 3
Definition of Rings
Properties of Rings
Homomorphisms
Chapter 4
Polynomial ring and division
Divisibility in F[x]
Irreducible Polynomials and Unique Factorization
Roots and Reducibility
Irreducible Criterions in Q[x]
Chapter 5
Congruence in F[x]
F[x]/(p(x)) when p(x) irreducible
Chapter 6
Ideals and Quotient Rings
Quotient Rings and Homomorphisms
Prime and Maximal Ideals
Chapter 7
Groups
Exams 📝
Acknowledgements
Explorer
Syllabus 📚
Calendar 📅
Homeworks ✏️
Notes 📓
Chapter 1
Division Algorithm
Proof of the Division Algorithm
Divisibility
Euclidean Algorithm
Prime Numbers
Fundamental Theorem of Arithmetic
Chapter 2
Congruence in the set of integers
The Set of Congruence Classes
Operations on Congruence Classes
Special Features of Z_p
Chapter 3
Definition of Rings
Properties of Rings
Homomorphisms
Chapter 4
Polynomial ring and division
Divisibility in F[x]
Irreducible Polynomials and Unique Factorization
Roots and Reducibility
Irreducible Criterions in Q[x]
Chapter 5
Congruence in F[x]
F[x]/(p(x)) when p(x) irreducible
Chapter 6
Ideals and Quotient Rings
Quotient Rings and Homomorphisms
Prime and Maximal Ideals
Chapter 7
Groups
Exams 📝
Acknowledgements
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Tag: Division-Algorithm-Theorem-Generalization
Tag: Division-Algorithm-Theorem-Generalization
1 item with this tag.
Dec 30, 2024
Proof of the Division Algorithm
Division-Algorithm-Theorem-Generalization
