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Advances in Commutative Algebra

Dedicated to David F. Anderson

  • Book
  • © 2019

Overview

Editors:
  1. Ayman Badawi

    1. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates

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  2. Jim Coykendall

    1. Department of Mathematical Sciences, Clemson University, Clemson, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Presents a collection of research from David F. Anderson as well as other experts in the field
  • Provides a valuable source of cutting-edge research in a number of subfields of commutative algebra
  • Is useful to graduate students and researchers

Part of the book series: Trends in Mathematics (TM)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xxii
    Download chapter PDF

  2. David Anderson and His Mathematics

    • D. D. Anderson
    Pages 1-6

  3. On \(\star \)-Semi-homogeneous Integral Domains

    • D. D. Anderson, Muhammad Zafrullah
    Pages 7-31

  4. t-Local Domains and Valuation Domains

    • Marco Fontana, Muhammad Zafrullah
    Pages 33-62

  5. Strongly Divided Pairs of Integral Domains

    • Ahmed Ayache, David E. Dobbs
    Pages 63-92

  6. Finite Intersections of Prüfer Overrings

    • Bruce Olberding
    Pages 93-111

  7. Strongly Additively Regular Rings and Graphs

    • Thomas G. Lucas
    Pages 113-134

  8. On t-Reduction and t-Integral Closure of Ideals in Integral Domains

    • Salah Kabbaj
    Pages 135-158

  9. Local Types of Classical Rings

    • L. Klingler, W. Wm. McGovern
    Pages 159-170

  10. How Do Elements Really Factor in \(\mathbb {Z}[\sqrt{-5}]\)?

    • Scott T. Chapman, Felix Gotti, Marly Gotti
    Pages 171-195

  11. David Anderson’s Work on Graded Integral Domains

    • Gyu Whan Chang, Hwankoo Kim
    Pages 197-216

  12. Divisor Graphs of a Commutative Ring

    • John D. LaGrange
    Pages 217-244

  13. Isomorphisms and Planarity of Zero-Divisor Graphs

    • Jesse Gerald Smith Jr.
    Pages 245-263
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Keywords

About this book

This book highlights the contributions of the eminent mathematician and leading algebraist David F. Anderson in wide-ranging areas of commutative algebra. It provides a balance of topics for experts and non-experts, with a mix of survey papers to offer a synopsis of developments across a range of areas of commutative algebra and outlining Anderson’s work. The book is divided into two sections—surveys and recent research developments—with each section presenting material from all the major areas in commutative algebra. The book is of interest to graduate students and experienced researchers alike.

Editors and Affiliations

  • Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates

    Ayman Badawi

  • Department of Mathematical Sciences, Clemson University, Clemson, USA

    Jim Coykendall

About the editors

AYMAN BADAWI is Professor at the Department of Mathematics and Statistics, the American University of Sharjah, the United Arab Emirates. He earned his Ph.D. in Algebra from the University of North Texas, USA, in 1993. He is an active member of the American Mathematical Society and honorary member of the Middle East Center of Algebra and its Applications. His research interests include commutative algebra, pi-regular rings, and graphs associated to rings.


JIM COYKENDALL is Professor of Mathematical Sciences at Clemson University, South Carolina, USA. He earned his Ph.D. from Cornell University in 1995, and has held various academic positions at the California Institute of Technology, the University of Tennessee, Cornell University, Lehigh University, and North Dakota State University. He has successfully guided 12 Ph.D. students. His research interests include commutative algebra and number theory.

Bibliographic Information

  • Book Title: Advances in Commutative Algebra

  • Book Subtitle: Dedicated to David F. Anderson

  • Editors: Ayman Badawi, Jim Coykendall

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-981-13-7028-1

  • Publisher: Birkhäuser Singapore

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

  • Copyright Information: Springer Nature Singapore Pte Ltd. 2019

  • Hardcover ISBN: 978-981-13-7027-4Published: 26 April 2019

  • eBook ISBN: 978-981-13-7028-1Published: 11 April 2019

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: XXII, 263

  • Number of Illustrations: 14 b/w illustrations, 2 illustrations in colour

  • Topics: Commutative Rings and Algebras, Combinatorics

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