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Rings Close to Regular

  • Book
  • © 2002

Overview

Authors:
  1. Askar Tuganbaev

    1. Moscow Power Engineering Institute, Technological University, Moscow, Russia

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Part of the book series: Mathematics and Its Applications (MAIA, volume 545)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
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  2. Some Basic Facts of Ring Theory

    • Askar Tuganbaev
    Pages 1-66

  3. Regular and Strongly Regular Rings

    • Askar Tuganbaev
    Pages 67-112

  4. Rings of Bounded Index and I 0-rings

    • Askar Tuganbaev
    Pages 113-152

  5. Semiregular and Weakly Regular Rings

    • Askar Tuganbaev
    Pages 153-186

  6. Max Rings and π-regular Rings

    • Askar Tuganbaev
    Pages 187-228

  7. Exchange Rings and Modules

    • Askar Tuganbaev
    Pages 229-278

  8. Separative Exchange Rings

    • Askar Tuganbaev
    Pages 279-314

  9. Back Matter

    Pages 315-350
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Keywords

About this book

Preface All rings are assumed to be associative and (except for nilrings and some stipulated cases) to have nonzero identity elements. A ring A is said to be regular if for every element a E A, there exists an element b E A with a = aba. Regular rings are well studied. For example, [163] and [350] are devoted to regular rings. A ring A is said to be tr-regular if for every element a E A, there is an element n b E A such that an = anba for some positive integer n. A ring A is said to be strongly tr-regular if for every a E A, there is a positive integer n with n 1 n an E a + An Aa +1. It is proved in [128] that A is a strongly tr-regular ring if and only if for every element a E A, there is a positive integer m with m 1 am E a + A. Every strongly tr-regular ring is tr-regular [38]. If F is a division ring and M is a right vector F-space with infinite basis {ei}~l' then End(MF) is a regular (and tr-regular) ring that is not strongly tr-regular. The factor ring of the ring of integers with respect to the ideal generated by the integer 4 is a strongly tr-regular ring that is not regular.

Reviews

From the reviews:

"This is the first monograph on rings close to von Neumann regular rings. … The book will appeal to readers from beginners to researchers and specialists in algebra; it concludes with an extensive bibliography." (Xue Weimin, Zentralblatt MATH, Vol. 1120 (22), 2007)

Authors and Affiliations

  • Moscow Power Engineering Institute, Technological University, Moscow, Russia

    Askar Tuganbaev

About the author

Askar Tuganbaev received his Ph.D. at the Moscow State University in 1978 and has been a professor at Moscow Power Engineering Institute (Technological University) since 1978. He is the author of three other monographs on ring theory and has written numerous articles on ring theory.

Bibliographic Information

  • Book Title: Rings Close to Regular

  • Authors: Askar Tuganbaev

  • Series Title: Mathematics and Its Applications

  • DOI: https://doi.org/10.1007/978-94-015-9878-1

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2002

  • Hardcover ISBN: 978-1-4020-0851-1Published: 30 September 2002

  • Softcover ISBN: 978-90-481-6116-4Published: 09 December 2010

  • eBook ISBN: 978-94-015-9878-1Published: 09 March 2013

  • Edition Number: 1

  • Number of Pages: XII, 350

  • Topics: Associative Rings and Algebras

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