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Item Details
| Title:
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RINGS CLOSE TO REGULAR
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| By: |
Askar A. Tuganbaev |
| Format: |
Paperback |
| List price:
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£90.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
9048161169 |
| ISBN 13: |
9789048161164 |
| Publisher: |
SPRINGER |
| Pub. date: |
8 December, 2010 |
| Edition: |
Softcover reprint of hardcover 1st ed. 2002 |
| Series: |
Mathematics and Its Applications 545 |
| Pages: |
350 |
| Synopsis: |
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. |
| Illustrations: |
XII, 350 p. |
| Publication: |
Netherlands |
| Imprint: |
Springer |
| Returns: |
Returnable |
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