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SUMMARY:Factorization in Some Interesting Integral Domains - Nathan Kaplan
DTSTART:20080312T140000Z
DTEND:20080312T150000Z
UID:TALK10958@talks.cam.ac.uk
CONTACT:Anton Evseev
DESCRIPTION:Let K be a number field and O_K its ring of integers. It is we
 ll known that\nO_K is a unique factorization domain if and only if the ide
 al class number\nof O_K is 1. A less well known result of Carlitz (1960)\,
  states that for\nevery x in O_K\, every factorization of x into irreducib
 les has the same\nlength if and only if the ideal class number of O_K is a
 t most 2.\n\nIn this talk we will focus on three types of domains where un
 ique\nfactorization does not generally hold: Arithmetic Congruence Monoids
 \, Block\nMonoids and Numerical Monoids. We will define some interesting\n
 factorization invariants and look at them in these three settings. We will
 \ngive many examples and few proofs and will state several unsolved proble
 ms\,\nso this talk should be accessible to a wide audience.
LOCATION:MR4\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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