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Mathematics and Its Applications

# Rings Close to Regular

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eBook $89.00 price for USA in USD (gross) • ISBN 978-94-015-9878-1 • Digitally watermarked, DRM-free • Included format: PDF • ebooks can be used on all reading devices • Immediate eBook download after purchase Hardcover$119.99
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Softcover $139.00 price for USA in USD • ISBN 978-90-481-6116-4 • Free shipping for individuals worldwide • Usually dispatched within 3 to 5 business days. 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. About the authors 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. 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) ## Table of contents (7 chapters) Table of contents (7 chapters) • Some Basic Facts of Ring Theory Pages 1-66 Tuganbaev, Askar • Regular and Strongly Regular Rings Pages 67-112 Tuganbaev, Askar • Rings of Bounded Index and I 0-rings Pages 113-152 Tuganbaev, Askar • Semiregular and Weakly Regular Rings Pages 153-186 Tuganbaev, Askar • Max Rings and π-regular Rings Pages 187-228 Tuganbaev, Askar ### Buy this book eBook$89.00
price for USA in USD (gross)
• ISBN 978-94-015-9878-1
• Digitally watermarked, DRM-free
• Included format: PDF
• ebooks can be used on all reading devices
Hardcover $119.99 price for USA in USD • ISBN 978-1-4020-0851-1 • Free shipping for individuals worldwide • Usually dispatched within 3 to 5 business days. Softcover$139.00
price for USA in USD
• ISBN 978-90-481-6116-4
• Free shipping for individuals worldwide
• Usually dispatched within 3 to 5 business days.

## Bibliographic Information

Bibliographic Information
Book Title
Rings Close to Regular
Authors
Series Title
Mathematics and Its Applications
Series Volume
545
2002
Publisher
Springer Netherlands