Rings Close to Regular (eBook)

A.A. Tuganbaev (Autor)

eBook Download: PDF

2013
Springer Netherlands (Verlag)
978-94-015-9878-1 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 9.3.2013
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• ISBN-10: 94-015-9878-9 / 9401598789
• ISBN-13: 978-94-015-9878-1 / 9789401598781