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Ring Theory (Math 113), Summer 2014

ring Theory (Math 113), Summer 2014 James McIvorUniversity of California, BerkeleyAugust 3, 2014 AbstractThese are some informal notes on rings and fields, used to teach Math 113 at UC Berkeley, Summer 2014. We go through the basic stuff: rings, homomorphisms, isomorphisms, ideals andquotient rings, division and (ir)reducibility, all heavy on the examples, mostly polynomial rings andtheir quotients. Some allusions to basic ideas from algebraic geometry are made along the we get into fields, culminating in a brief exposure to the basic ideas of galois Basic Examples and Examples.

10 Field Automorphisms and The Galois Group 36 ... 12 Fundamental Theorem of Galois Theory 43 ... This is an extension of the previous ring, too. In fact you can continue adding variables to get larger and larger rings. 6. Z=nZ: The integers mod n. These are equivalence classes of the integers under the equivalence

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