Rings close to regular
著者
書誌事項
Rings close to regular
（Mathematics and its applications, v. 545）
Kluwer Academic, c2002
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注記
Includes bibliographical references (p. [315]-347) and index
内容説明・目次
内容説明
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.
目次
Preface. Symbols. 1. Some Basic Facts of Ring Theory. 2. Regular and Strongly Regular Rings. 3. Rings of Bounded Index and Io-rings. 4. Semiregular and Weakly Regular Rings. 5. Max Rings and pi-regular Rings. 6. Exchange Rings and Modules. 7. Separative Exchange Rings. Bibliography. Index.
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