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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 .. of a ring .. elements in a ring ..52 Subrings; ; Adjoining Elements.

8 Field Extensions 30 ... Next lecture 1.1 Preliminary Examples A ring is just a set where you can add, subtract, and multiply. In some rings you can divide, and in ... this ring consists of what are called \formal power series" with entries in Q (the rational numbers). A power series is just a polynomial with (possibly) in nitely many terms ...

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