Rings Close to Regular

ISBN-13: 9781402008511 / Angielski / Twarda / 2002 / 350 str.

Askar A. Tuganbaev;Tuganbaev; A. a. Tuganbaev

Opis

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 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.

Recenzje

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)

Spis treści

Preface. Symbols. 1. Some Basic Facts of Ring Theory. 2. Regular and Strongly Regular Rings. 3. Rings of Bounded Index and Io-rings. 4. Semiregular and Weakly Regular Rings. 5. Max Rings and pi-regular Rings. 6. Exchange Rings and Modules. 7. Separative Exchange Rings. Bibliography. Index.

O autorze

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.