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# revf - Math 4124 Wednesday May 4 Final Review The exam is...

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Math 4124 Wednesday, May 4 Final Review The exam is on Wednesday May 11, 10:05 a.m. to 12:05 p.m. in Smyth 331. It is compre- hensive (includes material from the first two tests). The material since the second test is Sections 5.1, 5.2, 7.1–6, and parts of sections 8.2, 8.3, 9.2. One of the problems will be identical to one of the ungraded homework problems since the second test. Topics since the second test include 1. Classification of finitely generated abelian groups: invariant factors and elementary divisors. 2. Definition of rings, subrings, ideals, homomorphisms, isomorphisms. 3. Isomorphic rings. 4. Direct product of rings, quotient rings. 5. Fundamental isomorphism theorem, ideal correspondence theorem. 6. Polynomial rings. 7. Definition of integral domains and fields. 8. Prime and maximal ideals. An ideal is maximal if and only if the corresponding quotient ring is a field. An ideal is prime if and only if the corresponding quotient ring is an integral domain. Maximal ideals are always prime.

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