| 書目名稱 | Rings Close to Regular | | 編輯 | Askar Tuganbaev | | 視頻video | http://file.papertrans.cn/831/830416/830416.mp4 | | 叢書名稱 | Mathematics and Its Applications | | 圖書封面 |  | | 描述 | 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. | | 出版日期 | Book 2002 | | 關(guān)鍵詞 | DEX; Exchange; Finite; K-theory; Maxima; algebra; eXist; maximum; proof; ring; ring theory | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-015-9878-1 | | isbn_softcover | 978-90-481-6116-4 | | isbn_ebook | 978-94-015-9878-1 | | copyright | Springer Science+Business Media Dordrecht 2002 |
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