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Selected Exercises in Algebra

Volume 2

  • Textbook
  • © 2022

Overview

Authors:
  1. Rocco Chirivì

    1. Department of Mathematics and Physics, University of Salento, Lecce, Italy

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  2. Ilaria Del Corso

    1. Department of Mathematics, University of Pisa, Pisa, Italy

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    You can also search for this author in PubMed   Google Scholar

  3. Roberto Dvornicich

    1. Department of Mathematics, University of Pisa, Pisa, Italy

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  • Collection of preliminary exercises providing the essential tools for solutions
  • Careful presentation of the content with uniform language and style
  • Comprehensive review of the relevant theory readily available for easy reference

Part of the book series: UNITEXT (UNITEXT, volume 140)

Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-xii
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  2. Theory

    • Rocco Chirivì, Ilaria Del Corso, Roberto Dvornicich
    Pages 1-88

  3. Exercises

    • Rocco Chirivì, Ilaria Del Corso, Roberto Dvornicich
    Pages 89-124

  4. Solutions

    • Rocco Chirivì, Ilaria Del Corso, Roberto Dvornicich
    Pages 125-284

  5. Back Matter

    Pages 285-290
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Keywords

About this book

This book, the second of two volumes, contains approximately 350 exercises in Algebra which have featured exam questions for the Algebraic Structure and Algebra I courses taught by the authors at the University of Pisa. Each exercise is presented together with one or more solutions, carefully written with consistent language and notation. A distinguishing feature of this book is the fact that each exercise is unique and requires some creative thinking to be solved. The themes covered in this volume are: group theory and Sylow theorems, commutative rings with an emphasis on unique factorisation, Gaussian integers, field extensions and Galois theory. The book includes a detailed section recalling relevant theory that can be used as a reference for study and revision. A list of preliminary exercises introduces the main techniques to be applied in solving the proposed exam questions. This volume is aimed at second year students in Mathematics and Computer science.

Authors and Affiliations

  • Department of Mathematics and Physics, University of Salento, Lecce, Italy

    Rocco Chirivì

  • Department of Mathematics, University of Pisa, Pisa, Italy

    Ilaria Del Corso, Roberto Dvornicich

About the authors

Rocco Chirivì obtained a degree in Mathematics from the University of Pisa in 1995; he earned his Diploma di Licenza from the Scuola Normale of Pisa in 1997, followed by his Diploma di Perfezionamento in 2000. He has been a researcher in Algebra at the University of Pisa from 2002 until 2012 and at the University of Salento until 2019; he is currently an associate professor in Geometry at the University of Salento. His main research focus is Representation Theory at the intersection between Algebra, Combinatorics and the geometry of varieties related to group actions.

Ilaria Del Corso attended the Corso di Perfezionamento at the Scuola Normale from 1990 to 1992 and has been an associate professor in Algebra at the University of Pisa since 2001. She has extensive teaching experience in Algebra and Algebraic Number Theory. Her research in Algebraic Number Theory concerns number fields and local fields, focusing in particular on the study oframification and on the Galois module structure of certain field extensions.

Roberto Dvornicich, having been a student at the Scuola Normale of Pisa, obtained a degree in Mathematics from the University of Pisa in 1972 and later attended the Corso di Perfezionamento at the Scuola Normale. He has been a full professor in Algebra at the University of Pisa since 1990. His main research interests lie within Algebraic Number Theory (arithmetic properties of number fields and local fields) and in Diophantine Analysis (algebraic equations over the integers or some number field).


Bibliographic Information

  • Book Title: Selected Exercises in Algebra

  • Book Subtitle: Volume 2

  • Authors: Rocco Chirivì, Ilaria Del Corso, Roberto Dvornicich

  • Translated by: Alessandra Caraceni

  • Series Title: UNITEXT

  • DOI: https://doi.org/10.1007/978-3-031-12651-2

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Softcover ISBN: 978-3-031-12650-5Published: 30 November 2022

  • eBook ISBN: 978-3-031-12651-2Published: 28 November 2022

  • Series ISSN: 2038-5714

  • Series E-ISSN: 2532-3318

  • Edition Number: 1

  • Number of Pages: XII, 290

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Algebra

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