{"product_id":"rings-close-to-regular-a-a-tuganbaev-9781402008511","title":"Rings Close to Regular","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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e A. a. Tuganbaev\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1402008511\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781402008511\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/30\/2002\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 350\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.70lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.96h x 6.28w x 0.79d","brand":"A. a. Tuganbaev","offers":[{"title":"Hardcover","offer_id":48444741353727,"sku":"9781402008511","price":54.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_40a7df8c-0459-47b7-b4bd-21a6fe809b2d.jpg?v=1777214243","url":"https:\/\/www.whiterainbookhouse.com\/products\/rings-close-to-regular-a-a-tuganbaev-9781402008511","provider":"WR Book House","version":"1.0","type":"link"}