Rings Close to Regular

1. Front Matter

   Pages i-xii

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2. Some Basic Facts of Ring Theory

   • Askar Tuganbaev

   Pages 1-66

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3. Regular and Strongly Regular Rings

   • Askar Tuganbaev

   Pages 67-112

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4. Rings of Bounded Index and I ₀-rings

   • Askar Tuganbaev

   Pages 113-152

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5. Semiregular and Weakly Regular Rings

   • Askar Tuganbaev

   Pages 153-186

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6. Max Rings and π-regular Rings

   • Askar Tuganbaev

   Pages 187-228

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7. Exchange Rings and Modules

   • Askar Tuganbaev

   Pages 229-278

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8. Separative Exchange Rings

   • Askar Tuganbaev

   Pages 279-314

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9. Back Matter

   Pages 315-350

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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.

• DEX
• Exchange
• Finite
• K-theory
• Maxima
• algebra
• eXist
• maximum
• proof
• ring
• ring theory

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)

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

  Askar Tuganbaev

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.

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