Rings Close to Regular is popular PDF and ePub book, written by A.A. Tuganbaev in 2013-03-09, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Rings Close to Regular can be Read Online from any device for your convenience.
Rings Close to Regular Book PDF Summary
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.
Detail Book of Rings Close to Regular PDF
- Author : A.A. Tuganbaev
- Release : 09 March 2013
- Publisher : Springer Science & Business Media
- ISBN : 9789401598781
- Genre : Mathematics
- Total Page : 363 pages
- Language : English
- PDF File Size : 8,5 Mb
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