Transcription of Ring Theory (Math 113), Summer 2014
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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 .. of Rings ..103 Kernels and kernel of a homomorphism .. on Ideals ..144 Quotient : Cosets.. Rings .. easy way to think about quotients of a polynomial ring .. Isomorphism Theorem ..175 Factorization; Reducibility; and Factorization inZ.
Ring Theory (Math 113), Summer 2014 James McIvor University of California, Berkeley August 3, 2014 Abstract These are some informal notes on rings and elds, used to teach Math 113 at UC Berkeley, Summer 2014. We go through the basic stu : …
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