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.
General
| Imprint: |
Springer
|
| Country of origin: |
Netherlands |
| Series: |
Mathematics and Its Applications, 545 |
| Release date: |
December 2010 |
| First published: |
2002 |
| Authors: |
A. a. Tuganbaev
|
| Dimensions: |
235 x 155 x 19mm (L x W x T) |
| Format: |
Paperback
|
| Pages: |
350 |
| Edition: |
Softcover reprint of hardcover 1st ed. 2002 |
| ISBN-13: |
978-90-481-6116-4 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Algebra >
General
|
| LSN: |
90-481-6116-9 |
| Barcode: |
9789048161164 |
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