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|a 9789401598781
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|a Tuganbaev, A.A.
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| 245 |
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|a Rings Close to Regular
|h Elektronische Ressource
|c by A.A. Tuganbaev
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|a 1st ed. 2002
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| 260 |
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|a Dordrecht
|b Springer Netherlands
|c 2002, 2002
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| 300 |
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|a XII, 350 p
|b online resource
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|a 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
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| 653 |
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|a Associative algebras
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| 653 |
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|a Associative rings
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| 653 |
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|a Associative Rings and Algebras
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|a eng
|2 ISO 639-2
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|b SBA
|a Springer Book Archives -2004
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|a Mathematics and Its Applications
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|a 10.1007/978-94-015-9878-1
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| 856 |
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|u https://doi.org/10.1007/978-94-015-9878-1?nosfx=y
|x Verlag
|3 Volltext
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|a 512.46
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|a 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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