MATH 120B: INTRO RINGS/FIELDS

Note 1: Definitions and Basic Properties of Rings

Note 2: Homomorphisms and Isomorphisms / Multiplicative Questions: Fields

Note 3: Integral Domains / Fermat's and Euler's Theorems

Note 4: The Field of Quotients of an Integral Domain / Rings of Polynomials

Note 5: Rings of Polynomials (continued) / Factorization of Polynomials over a Field

Note 6: Homomorphisms and Factor Rings

Note 7: Prime and Maximal Ideals

Note 8: Prime and Maximal Ideals (continued) / Introduction to Extension Fields

Note 9: Introduction to Extension Fields (continued)

Note 10: Vector Spaces / Algebraic Extensions

Quiz 1: Definition of Rings

Quiz 2: Ring Homomorphisms / Zero Divisors and Units / Multiplicative Questions: Fields

Quiz 3: Zero Divisors / Characteristics / Fermat's and Euler's Theorems

Quiz 4: The Field of Quotients of an Integral Domain / Rings of Polynomials

Quiz 5: Rings of Polynomials / Factorization of Polynomials over a Field

Take Home Quiz 6: Homomorphisms

Quiz 7: Factor Rings

Quiz 8: Prime and Maximal Ideals

Quiz 9: Introduction to Extension Fields

Quiz 10: Vector Spaces / Algebraic Extensions