Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Constantin Nastasescu and Freddy van Oystaeyen
Title: Dimensions of ring theory
Additional book information: D. Reidel Publishing Company, Dordrecht, Boston, Lancaster and Tokyo, 1987, xi + 360 pp., $74.00. ISBN 90-277-2461-x.

References [Enhancements On Off] (What's this?)

  • 1. I. M. Gelfand and A. A, Kirillov, On fields connected with the enveloping algebras of Lie algebras (Russian), Dokl. Akad. Nauk SSSR 167 (1966), 503-505; [Translation: Soviet Math. Dokl. 7 (1966), 407-409]. MR 195912
  • 2. I. M. Gelfand and A. A, Kirillov, Sur les corps liés aux algèbres enveloppantes des algèbres de Lie, Publ. Math. I.H.E.S. 31 (1966), 5-19. MR 207918
  • 3. A. W. Goldie, The structure of prime rings under ascending chain conditions, Proc. London Math. Soc. (3) 8 (1958), 589-608. MR 103206
  • 4. A. Joseph, Goldie rank in the enveloping algebra of a semisimple Lie algebra. I, II, J. Algebra 65 (1980), no. 2, 269–283, 284–306. MR 585721, https://doi.org/10.1016/0021-8693(80)90217-3
  • 5. G. Krause, On the Krull-dimension of left noetherian left Matlis-rings, Math. Z. 118 (1970), 207-214. MR 279124
  • 6. Günter R. Krause and Thomas H. Lenagan, Growth of algebras and Gelfand-Kirillov dimension, Revised edition, Graduate Studies in Mathematics, vol. 22, American Mathematical Society, Providence, RI, 2000. MR 1721834
  • 7. W. Krull, Primidealketten in allgemeinen Ringbereichen, Sitzungsberichte Heidelberg. Akad. Wissenschaft (1928) 7. Abhandl., 3-14.
  • 8. Charles Lanski, Gabriel dimension and rings with involution, Houston J. Math. 4 (1978), no. 3, 397–415. MR 514253
  • 9. J. C. McConnell and J. C. Robson, Noncommutative Noetherian rings, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1987. With the cooperation of L. W. Small; A Wiley-Interscience Publication. MR 934572
  • 10. Emmy Noether, Eliminationstheorie und allgemeine Idealtheorie, Math. Ann. 90 (1923), no. 3-4, 229–261 (German). MR 1512173, https://doi.org/10.1007/BF01455443
  • 11. Donald S. Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. MR 470211
  • 12. R. Rentschler and P. Gabriel, Sur la dimension des anneaux et ensembles ordonnés, C. R. Acad. Sci. Paris Sér. A 265 (1967), 712-715. MR 224644
  • 13. J. T. Stafford, Generating modules efficiently: algebraic 𝐾-theory for noncommutative Noetherian rings, J. Algebra 69 (1981), no. 2, 312–346. MR 617082, https://doi.org/10.1016/0021-8693(81)90208-8
  • 14. Patrice Tauvel, Sur les quotients premiers de l’algèbre enveloppante d’une algèbre de Lie résoluble, Bull. Soc. Math. France 106 (1978), no. 2, 177–205 (French). MR 507749

Review Information:

Reviewer: K. R. Goodearl
Journal: Bull. Amer. Math. Soc. 20 (1989), 107-112
DOI: https://doi.org/10.1090/S0273-0979-1989-15718-2
American Mathematical Society