Unformatted text preview: Exam 3 Review What are you expected to know for exam 3? • Deﬁnitions: – ring – ﬁeld – integral domain – ideal, maximal ideal – quotient ring – polynomial ring – ﬁeld of fractions – ring homomorphism – characteristic of a ﬁeld – extension ﬁeld and splitting ﬁeld • Elementary properties of rings • Isomorphism Theorems and Correspondence Theorem • Properties of polynomial rings • Eisenstein’s Criterion • The Mod p Irreducibility Test • The fundamental theorem of ﬁeld theory • The structure of splitting ﬁelds; the existence and uniqueness of splitting ﬁelds • How to construct ﬁeld extensions What will the format for exam 3 be? There will be 4 questions totalling 40 points that everyone will answer. These will focus on the major concepts from the material. There will also be 5 questions, worth 20 points each. You will have your choice of which 3 of these to answer. ...
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 Spring '11
 Johnson
 Algebra, Fractions, Ring theory, polynomial rings, Splitting Fields

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