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 .. of Rings ..103 Kernels and kernel of a homomorphism .. on Ideals ..144 Quotient : Cosets.. Rings.

or not, so that the series n!xn is perfectly good, even though you never talk about it in calcu-lus because it only converges when x = 0. Because of this possible non-convergence, we can’t think of these power series as functions, and we think of the x as a \formal variable", rather than something for which we can substitute a numerical value.

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  Theory, Ring, Calcu, Ring theory, Cal culus

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