Difference between revisions of "Math 372: Abstract Algebra 2."

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(Minimal learning outcomes)
(Minimal learning outcomes)
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#* Irreducible polynomials
#* Irreducible polynomials
#* Field of fractions of a domain
#* Field of fractions of a domain
# Field Theory
# Field Theory
#* Extensions of fields
#* Extensions of fields

Revision as of 13:37, 24 May 2010

Catalog Information


Abstract Algebra 2.

(Credit Hours:Lecture Hours:Lab Hours)



F, W


Math 371.


Fields, Galois theory, solvability of polynomials by radicals.

Desired Learning Outcomes


Minimal learning outcomes

Students should achieve mastery of the topics listed below. This means that they should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the below concepts, related to, but not identical to, statements proven by the text or instructor.

  1. Ring Theory
    • Basic Definitions
    • Examples of rings (both commutative and noncommutative)
    • Ideals
    • Ring homomorphisms
    • Quotient rings
    • Prime and maximal ideals
    • Polynomial rings over fields
    • Factorization in polynomial rings
    • Irreducible polynomials
    • Field of fractions of a domain
  2. Field Theory
    • Extensions of fields
    • Field extensions via quotients in polynomial rings
    • Automorphisms of fields
    • Field of characteristic 0 and prime characteristic
    • Galois extensions and Galois groups
    • The Galois correspondence
    • Independence of characters
    • Fundamental Theorem of Galois Theory
    • Fundamental Theorem of Algebra
    • Roots of unity
    • Solvability by radicals
    • Insolvability of the quintic

Additional topics

Courses for which this course is prerequisite