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Rings Close to Regular - A.A. Tuganbaev

Rings Close to Regular

(Autor)

Buch | Softcover
350 Seiten
2010 | Softcover reprint of hardcover 1st ed. 2002
Springer (Verlag)
978-90-481-6116-4 (ISBN)
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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. 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.
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.

Askar Tuganbaev received his Ph.D. at the Moscow State University in 1978 and has been a professor at Moscow Power Engineering Institute (Technological University) since 1978. He is the author of three other monographs on ring theory and has written numerous articles on ring theory.

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.

Erscheint lt. Verlag 9.12.2010
Reihe/Serie Mathematics and Its Applications ; 545
Zusatzinfo XII, 350 p.
Verlagsort Dordrecht
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
ISBN-10 90-481-6116-9 / 9048161169
ISBN-13 978-90-481-6116-4 / 9789048161164
Zustand Neuware
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