BEGIN:VCALENDAR VERSION:2.0 PRODID:-//jEvents 2.0 for Joomla//EN CALSCALE:GREGORIAN METHOD:PUBLISH BEGIN:VTIMEZONE TZID:Europe/Budapest END:VTIMEZONE BEGIN:VEVENT 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:20211028T014334Z DTSTART;TZID=Europe/Budapest:20180418T100000 DTEND;TZID=Europe/Budapest:20180418T120000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR