Exam3Review - Exam 3 Review What are you expected to know...

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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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