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DTSTART:19700329T010000
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CATEGORIES:Junior Algebra and Number Theory seminar
SUMMARY:Factorization in Some Interesting Integral Domains
- Nathan Kaplan
DTSTART;TZID=Europe/London:20080312T140000
DTEND;TZID=Europe/London:20080312T150000
UID:TALK10958AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/10958
DESCRIPTION:Let K be a number field and O_K its ring of intege
rs. It is well known that\nO_K is a unique factori
zation domain if and only if the ideal class numbe
r\nof O_K is 1. A less well known result of Carlit
z (1960)\, states that for\nevery x in O_K\, every
factorization of x into irreducibles has the same
\nlength if and only if the ideal class number of
O_K is at most 2.\n\nIn this talk we will focus on
three types of domains where unique\nfactorizatio
n does not generally hold: Arithmetic Congruence M
onoids\, Block\nMonoids and Numerical Monoids. We
will define some interesting\nfactorization invari
ants and look at them in these three settings. We
will\ngive many examples and few proofs and will s
tate several unsolved problems\,\nso this talk sho
uld be accessible to a wide audience.
LOCATION:MR4\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
CONTACT:Anton Evseev
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