MA3L307
Undergraduate (ITEP)
· Generally offered: Spring
Rings and Fields
L 3 T 1 P 0 Credits 4 Hours 4
Unit I: Definition, examples and properties of rings, Subrings, Ideals, Prime and maximal ideals, Ring homomorphism, Isomorphism theorems.
Unit II: Quotient Rings, Rings of fractions, Chinese Remainder Theorem, Polynomial Rings, Integral domain, Euclidean Domain, Principal Ideal Domain, Unique Factorization Domain, Gauss’ Lemma, Irreducibility criterion, Eisenstein’s criterion.
Unit III: Definition, examples and properties of fields, Characteristic of a field, Field extensions, Algebraic and transcendental elements.
Unit IV: Splitting fields, Separable and normal extensions, Primitive roots of unity, Cyclotomic polynomials, Finite fields.
Full syllabus document →
Unit II: Quotient Rings, Rings of fractions, Chinese Remainder Theorem, Polynomial Rings, Integral domain, Euclidean Domain, Principal Ideal Domain, Unique Factorization Domain, Gauss’ Lemma, Irreducibility criterion, Eisenstein’s criterion.
Unit III: Definition, examples and properties of fields, Characteristic of a field, Field extensions, Algebraic and transcendental elements.
Unit IV: Splitting fields, Separable and normal extensions, Primitive roots of unity, Cyclotomic polynomials, Finite fields.
0 questions tagged to this course
No questions tagged to this course yet — ask one.