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＜電子ブック＞
Rings Close to Regular / by A.A. Tuganbaev
(Mathematics and Its Applications ; 545)

版	1st ed. 2002.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2002
本文言語	英語
大きさ	XII, 350 p : online resource
著者標目	*Tuganbaev, A.A author SpringerLink (Online service)
件　名	LCSH:Associative rings LCSH:Associative algebras FREE:Associative Rings and Algebras
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-94-015-9878-1

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