Bulletin of the American Mathematical Society

MathSciNet review: 1567733
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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.

I. M. Gel′fand and A. A. Kirillov, On fields connected with the enveloping algebras of Lie algebras, Dokl. Akad. Nauk SSSR 167 (1966), 503–505 (Russian). MR 0195912

I. M. Gelfand and A. A. Kirillov, Sur les corps liés aux algèbres enveloppantes des algèbres de Lie, Inst. Hautes Études Sci. Publ. Math. 31 (1966), 5–19 (French). MR 207918

A. W. Goldie, The structure of prime rings under ascending chain conditions, Proc. London Math. Soc. (3) 8 (1958), 589–608. MR 103206, DOI 10.1112/plms/s3-8.4.589

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, DOI 10.1016/0021-8693(80)90217-3

Günter Krause, On the Krull-dimension of lift noetherian left Matlis-rings, Math. Z. 118 (1970), 207–214. MR 279124, DOI 10.1007/BF01113344

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, DOI 10.1090/gsm/022

7.

W. Krull, Primidealketten in allgemeinen Ringbereichen, Sitzungsberichte Heidelberg. Akad. Wissenschaft (1928) 7. Abhandl., 3-14.

Charles Lanski, Gabriel dimension and rings with involution, Houston J. Math. 4 (1978), no. 3, 397–415. MR 514253

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

Emmy Noether, Eliminationstheorie und allgemeine Idealtheorie, Math. Ann. 90 (1923), no. 3-4, 229–261 (German). MR 1512173, DOI 10.1007/BF01455443

Donald S. Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977. MR 0470211

Rudolf Rentschler and Pierre Gabriel, Sur la dimension des anneaux et ensembles ordonnés, C. R. Acad. Sci. Paris Sér. A-B 265 (1967), A712–A715 (French). MR 224644

J. T. Stafford, Generating modules efficiently: algebraic $K$-theory for noncommutative Noetherian rings, J. Algebra 69 (1981), no. 2, 312–346. MR 617082, DOI 10.1016/0021-8693(81)90208-8

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

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 0195912

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, J. Algebra 65 (1980), 269-283. MR 585721

5.

G. Krause, On the Krull-dimension of left noetherian left Matlis-rings, Math. Z. 118 (1970), 207-214. MR 279124

6.

G. R. Krause and T. H. Lenagan, Growth of algebras and Gelfand-Kirillov dimension, Research Notes in Math., no. 116, Boston-London-Melbourne, Pitman Press, 1985. MR 1721834

7.

W. Krull, Primidealketten in allgemeinen Ringbereichen, Sitzungsberichte Heidelberg. Akad. Wissenschaft (1928) 7. Abhandl., 3-14.

8.

C. Lanski, Gabriel dimension and rings with involution, Houston J. Math. 4 (1978), 397-415. MR 514253

9.

J. C. McConnell and J. C. Robson, Noncommutative Noetherian rings, Wiley-Interscience, Chichester-New York-Brisbane-Toronto-Singapore, 1987. MR 934572

10.

E. Noether, Eliminationstheorie und allgemeine Idealtheorie, Math. Ann. 90 (1923), 229-261. MR 1512173

11.

D. S. Passman, The algebraic structure of group rings, Wiley-Interscience, 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-theoryfor noncommutative Noetherian rings, J. Algebra 69 (1981), 312-346. MR 617082

14.

P. Tauvel, Sur les quotients premiers de l'algèbre enveloppante d'une algèbre de Lie résoluble, Bull. Soc. Math. France 106 (1978), 177-205. MR 507749