
Rings Close to Regular
A.A. Tuganbaev(Author)
Springer (Publisher)
Published on 9. December 2010
Book
Paperback/Softback
XII, 350 pages
978-90-481-6116-4 (ISBN)
Description
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 / Votes
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)
More details
Series
Edition
Softcover reprint of hardcover 1st ed. 2002
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Illustrations
XII, 350 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 20 mm
Weight
557 gr
ISBN-13
978-90-481-6116-4 (9789048161164)
DOI
10.1007/978-94-015-9878-1
Schweitzer Classification
Other editions
Additional editions

A.A. Tuganbaev
Rings Close to Regular
Book
09/2002
1st Edition
Kluwer Academic Publishers
€53.49
Shipment within 15-20 days
Person
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.
Content
1 Some Basic Facts of Ring Theory.- 2 Regular and Strongly Regular Rings.- 3 Rings of Bounded Index and I0-rings.- 4 Semiregular and Weakly Regular Rings.- 5 Max Rings and ?-regular Rings.- 6 Exchange Rings and Modules.- 7 Separative Exchange Rings.