Rings Close to Regular
Produktnummer:
18e70807971cfb4feaa784168d4a7400d2
Autor: | Tuganbaev, A.A. |
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Themengebiete: | DEX Exchange Finite K-theory Maxima algebra eXist maximum proof ring |
Veröffentlichungsdatum: | 09.12.2010 |
EAN: | 9789048161164 |
Sprache: | Englisch |
Seitenzahl: | 350 |
Produktart: | Kartoniert / Broschiert |
Verlag: | Springer Netherland |
Produktinformationen "Rings Close to Regular"
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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