Rings Close to Regular (Mathematics and Its Applications, 545)
ISBN-13:
9789048161164
ISBN-10:
9048161169
Edition:
Softcover reprint of hardcover 1st ed. 2002
Author:
A.A. Tuganbaev
Publication date:
2010
Publisher:
Springer
Format:
Paperback
362 pages
Category:
Pure Mathematics
,
Mathematics
FREE US shipping
Book details
ISBN-13:
9789048161164
ISBN-10:
9048161169
Edition:
Softcover reprint of hardcover 1st ed. 2002
Author:
A.A. Tuganbaev
Publication date:
2010
Publisher:
Springer
Format:
Paperback
362 pages
Category:
Pure Mathematics
,
Mathematics
Summary
Rings Close to Regular (Mathematics and Its Applications, 545) (ISBN-13: 9789048161164 and ISBN-10: 9048161169), written by authors
A.A. Tuganbaev, was published by Springer in 2010.
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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.
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