Monogenity and Power Integral Bases

Contemporary Methods and Results
Erscheinungsjahr 2027
ISBN: 978-3-032-47157-4
Verlag: Birkhäuser

Buch, Englisch, 122 Seiten, Format (B × H): 168 mm x 240 mm

Reihe: Frontiers in Mathematics

This book provides an overview of recent results on the monogenity of polynomials and number fields, including binomials, trinomials, and quadrinomials. The author also offers an introduction to the number-theoretic technique used to attain these results in monogenity theory. In addition to general methods, chapters present several algorithms for calculating generators of power integral bases in various number fields. With the necessary background information included, readers will find this a self-contained resource on this timely topic. will be ideal for graduate students and researchers interested in this active area of algebraic number theory. Readers should have an understanding of number fields and basic algebraic approaches to Diophantine equations.

Zielgruppe

Research

Autoren/Hrsg.

Gaál, István

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

Auxiliary Tools.- Monogenity of binomials — Pure fields.- Monogenity of trinomials, quadrinomial, etc..- Monogenity of polynomial compositions.- Monogenity of some families of polynomials.

Über Autor(innen)

The author is a professor in mathematics at the University of Debrecen, Hungary. He started to investigate monogenity properties of number fields in the beginning of the nineties. He has published more than a hundred papers and two books. In 2021 he has started a series of online conferences, concentrating on the topic of "Monogenity and power integral bases". The online conferences made possible to share recent result, to make contacts and to start collaborations. The author is very thankful to the participants of these meetings and hope that also in the future the meetings will support investigations in monogenity theory of number fields. The present book contains a collection of results, mostly related to these meetings.