On the Joseph-small additivity principle for goldie ranks. A study on extensions of noetherian rings with applications to enveloping algebras
Compositio Mathematica, Volume 47 (1982) no. 1, p. 3-29
@article{CM_1982__47_1_3_0,
     author = {Borho, Walter},
     title = {On the Joseph-small additivity principle for goldie ranks. A study on extensions of noetherian rings with applications to enveloping algebras},
     journal = {Compositio Mathematica},
     publisher = {Martinus Nijhoff Publishers},
     volume = {47},
     number = {1},
     year = {1982},
     pages = {3-29},
     zbl = {0502.17007},
     mrnumber = {668778},
     language = {en},
     url = {http://www.numdam.org/item/CM_1982__47_1_3_0}
}
Borho, Walter. On the Joseph-small additivity principle for goldie ranks. A study on extensions of noetherian rings with applications to enveloping algebras. Compositio Mathematica, Volume 47 (1982) no. 1, pp. 3-29. http://www.numdam.org/item/CM_1982__47_1_3_0/

[1] I.N. Bernstein: Modules over a ring of differential operators. Study of the fundamental solutions of equations with constant coefficients. Funct. Anal. Appl. 5 (1971) 89-101. | MR 290097 | Zbl 0233.47031

[2] W. Borho, P. Gabriel, and R. Rentschler: Primideale in Einhüllenden auflösbarer Lie-Algebren. Springer LN 357 (1973). | MR 376790 | Zbl 0293.17005

[3] W. Borho and J.C. Jantzen: Über primitive Ideale in der Einhüllenden einer halbeinfachen Lie-Algebra. Invent. Math. 39 (1977) 1-53. | MR 453826 | Zbl 0327.17002

[4] W. Borho and H. Kraft: Über die Gelfand-Kirillov-Dimension. Math. Ann. 220 (1976) 1-24. | MR 412240 | Zbl 0306.17005

[5] W. Borho and R. Rentschler: Oresche Teilmengen in Einhüllenden Algebren. Math. Ann. 217 (1975) 201-210. | MR 401853 | Zbl 0297.17004

[6] N. Bourbaki: Algèbre commutative, Chap. 3 et 4. Paris, Hermann 1967.

[7] P. Gabriel and R. Rentschler: Sur la dimension des anneaux et ensembles ordonnés. C.R. Acad. Sci. Paris 265 (1967) 712-715. | MR 224644 | Zbl 0155.36201

[8] I.M. Gelfand and A.A. Kirillov: Sur les corps liés aux algèbres enveloppantes des algèbres de Lie. Publ. IHES 31 (1966) 5-19. | Numdam | MR 207918 | Zbl 0144.02104

[9] A.W. Goldie: The structure of Noetherian Rings, Springer LN 245 (1972) 213-321. | MR 393118 | Zbl 0237.16004

[10] R. Gordon and J.C. Robson: Krull Dimension. Mem. AMS 133 (1973). | MR 352177 | Zbl 0269.16017

[11] A. Joseph and L.W. Small: An additivity principle for Goldie rank. Israel J. Math. 31 (1978) 105-114. | MR 516246 | Zbl 0395.17010

[12] A. Joseph: Towards the Jantzen conjecture I, II. Compos. Math. 40 (1980) 35-67. | Numdam | MR 558258 | Zbl 0424.17004

[13] A. Joseph: Kostant's problem, Goldie rank and the Gelfand-Kirillov conjecture. Invent. Math. 56 (1980) 191-213. | MR 561970 | Zbl 0446.17006

[14] A. Joseph: Goldie rank in the enveloping algebra of a semisimple Lie algebra, I, II. J. Algebra 66 (1980) 269-306. | MR 585721 | Zbl 0441.17004

[15] G. Krause, T.H. Lenagan and J.T. Stafford: Ideal invariance and Artinian quotient rings. J. Algebra 55 (1978) 145-154. | MR 515765 | Zbl 0408.16002

[16] L. Levy: Torsion-free and divisible modules over non-integral domains. Canad. J. Math. 15 (1963) 132-151. | MR 142586 | Zbl 0108.04001

[17] L.W. Small: Orders in Artinian rings. J. Algebra 4 (1966) 13-41. | MR 200300 | Zbl 0147.28703

[18] P.F. Smith: On two-sided Artinian quotient rings. Glasgow Math. J. 13 (1972) 159-163. | MR 316488 | Zbl 0243.16001

[19] J.T. Stafford: Regular elements of Noetherian rings. Proc. 1978 Antwerp Conference, Marcel Dekker Co., New York. | MR 563299

[20] J.T. Stafford: Noetherian full quotient rings. preprint, Cambridge-La Jolla 1980. | MR 656242

[21] J.T. Stafford: Stable structure of non-commutative Noetherian rings. J. Algebra 47 (1977) 244-267. | MR 447335 | Zbl 0391.16009

[22] D. Vogan: A generalized τ-invariant for the primitive spectrum of a semisimple Lie-algebra. Math. Ann. 242 (1979) 209-224. | Zbl 0387.17007

[23] A. Joseph: Dimension en algèbre non-commutative, Cours de troisième cycle, Paris 1980 (unpublished notes).

[24] G. Bergman: Gel'fand-Kirillov-dimension can go up in extension modules. Communications in Algebra (to appear), preprint, Berkeley 1981. | MR 630326 | Zbl 0466.16023

[25] R. Gordon: Artinian quotient rings of FBN-rings. J. Algebra 35 (1975) 304-307. | MR 384851 | Zbl 0307.16003

[26] W. Borho: Invariant dimension and restricted extension of Noetherian rings; preprint, Wuppertal, June 1981 (to appear in Séminaire d'Algèbre (Dubreil-Malliavin), Springer Lecture Notes in Mathematics). | MR 662252 | Zbl 0482.16015