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UID:22u30ibnlaa9elulccdqdm8frg@google.com
CATEGORIES:{lang hu}Algebra szeminárium{/lang}{lang en}Algebra seminar{/lang}
SUMMARY:István Gaál (University of Debrecen): Thue equations and monogenity of algebraic number fields
LOCATION:Bolyai Intézet, I. emelet, Riesz terem, Aradi Vértanúk tere 1., Szeged
DESCRIPTION;ENCODING=QUOTED-PRINTABLE:Abstract. An algebraic field K is monogene if its ring of integers is a sim
ple ring extension of Z. In this case the powers of the generating element
form an integral basis of K, called power integral basis.\n\nIt is a classi
cal problem of algebraic number theory to decide if a number field is monog
ene and to determine all generators of its power integral bases. The proble
m can be reduced to the resolution of a certain type of diophantine equatio
ns called index form equations.\n\nIn some cases these index form equations
are Thue equations or can be solved by using Thue equations (and its gener
alizations). Therefore we explain the basic methods of solving one of the m
ost classical types of diophantine equations, the Thue equations.\n\nSome r
ecent results are on infinite parametric families of number fields and on t
he problem of monogenity and power integral bases in these families of fiel
ds.
DTSTAMP:20200712T110628Z
DTSTART;TZID=Europe/Budapest:20180418T100000
DTEND;TZID=Europe/Budapest:20180418T120000
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