the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

No abstract

Let m be a square-free integer (m = 0, ±1). We show that the structure of the integral bases of the fields K = Q( n √ m) are periodic in m. For 3 ≤ n ≤ 9 we show that the period length is n 2 . We explicitly describe the integral bases, and for n = 3, 4, 5, 6, 8 we explicitly calculate the index forms of K. This enables us in many cases to characterize the monogenity of these fields. Using the explicit form of the index forms yields a new technic that enables us to derive new results on monogenity and to get several former results as easy consequences. For n = 4, 6, 8 we give an almost complete characterization of the monogenity of pure fields.

No abstract

No abstract