Rings Close to Regular

2002
ISBN: 978-1-4020-0851-1
Verlag: Springer Netherlands

Buch, Englisch, Band 545, 350 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1530 g

Reihe: Mathematics and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Tuganbaev, A. A.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

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.