Bibliographic Information

Rings close to regular

by Askar A. Tuganbaev

(Mathematics and its applications, v. 545)

Kluwer Academic, c2002

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Note

Includes bibliographical references (p. [315]-347) and index

Description and Table of Contents

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.

Table of Contents

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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Details

  • NCID
    BA59476209
  • ISBN
    • 1402008511
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Dordrecht
  • Pages/Volumes
    xii, 350 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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