Rings Close to Regular: 545 (Mathematics and Its Applications) - Softcover

Tuganbaev, Askar

Softcover

ISBN 10: 9048161169 ISBN 13: 9789048161164

Verlag: Springer, 2010

Über diesen Titel

Críticas:

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)

Reseña del editor:

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.

Über diese Auflage

• Verlag: Springer
• Erscheinungsdatum: 2010
• ISBN 10: 9048161169
• ISBN 13: 9789048161164
• Einband: Tapa blanda
• Anzahl der Seiten: 364