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TZID:Europe/Budapest
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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.
It is a
classical problem of algebraic number theory to decide if a number field is
monogene and to determine all generators of its power integral bases. The
problem can be reduced to the resolution of a certain type of diophantine e
quations called index form equations.
In some cases these index fo
rm equations are Thue equations or can be solved by using Thue equations (a
nd its generalizations). Therefore we explain the basic methods of solving
one of the most classical types of diophantine equations, the Thue equation
s.
Some recent results are on infinite parametric families of numb
er fields and on the problem of monogenity and power integral bases in thes
e families of fields.
DTSTAMP:20240328T192420Z
DTSTART;TZID=Europe/Budapest:20180418T100000
DTEND;TZID=Europe/Budapest:20180418T120000
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