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Rings Close to Regular

by A. A. Tuganbaev
Save 35% Save 35%
Current price ₹3,639.00
Original price ₹5,597.00
Original price ₹5,597.00
Original price ₹5,597.00
(-35%)
₹3,639.00
Current price ₹3,639.00

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Book cover type: Paperback
  • ISBN13: 9789048161164
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 350
  • Original Price: EUR 49.99
  • Language: English
  • Edition: N/A
  • Item Weight: 555 grams
  • BISAC Subject(s): Algebra / Abstract and Algebra / General

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.

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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