Ore sets in enveloping algebras
Brown, Kenneth A.
Compositio Mathematica, Tome 53 (1984), p. 347-367 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1984-01-01
@article{CM_1984__53_3_347_0,
     author = {Brown, Kenneth A.},
     title = {Ore sets in enveloping algebras},
     journal = {Compositio Mathematica},
     volume = {53},
     year = {1984},
     pages = {347-367},
     mrnumber = {768829},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1984__53_3_347_0}
}

Brown, Kenneth A. Ore sets in enveloping algebras. Compositio Mathematica, Tome 53 (1984) pp. 347-367. http://gdmltest.u-ga.fr/item/CM_1984__53_3_347_0/

[1] H. Bass, Big projective modules are free. Illinois J. Math. 7 (1963) 24-31. | MR 143789 | Zbl 0115.26003

[2] H. Bass, A lgebraic K- theory. Benjamin (New York) 1968. | MR 249491

[3] J.-E. Bjork, Rings of Differential Operators. North Holland (Amsterdam) 1979. | MR 549189 | Zbl 0499.13009

[4] W. Borho, P. Gabriel and R. Rentschler, Primideale in Einhullenden auflösbarer Lie-Algebren. Lecture Notes in Mathematics vol. 357, Springer-Verlag (Berlin) 1973. | MR 376790 | Zbl 0293.17005

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

[6] K.A. Brown, Module extensions over Noetherian rings. J. Algebra 69 (1981) 247-260. | MR 617075 | Zbl 0471.16012

[7] K.A. Brown, Localisation, bimodules and injective modules for enveloping algebras of solvable Lie algebras. Bull des Sciences Math. 107 (1983) 225-251. | MR 719266 | Zbl 0524.16002

[8] J.H. Cozzens and C. Faith, Simple Noetherian Rings. Cambridge Univ. Press (Cambridge) 1975. | MR 396660 | Zbl 0314.16001

[9] J. Dixmier, Algèbres Enveloppantes. Gauthier-Villars (Paris) 1974. | MR 498737 | Zbl 0308.17007

[10] M. Duflo, Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semisimple. Annals of Math. 105 (1977) 107-120. | MR 430005 | Zbl 0346.17011

[11] J.E. Humphreys, Introduction to Lie Algebras and Representation Theory. Springer-Verlag (New York) 1972. | MR 323842 | Zbl 0254.17004

[12] A.V. Jategaonkar, Localisation in Noetherian Rings. Memoir, to appear. | Zbl 0589.16014

[13] A.V. Jategaonkar, Noetherian bimodules, primary decomposition, and Jacobson's conjecture. J. Algebra 71 (1981) 379-400. | MR 630604 | Zbl 0478.16011

[14] A.V. Jategaonkar, Localisation in non-commutative Noetherian rings, Preprint.

[15] D.A. Jordan, A left Noetherian, right Ore domain which is not right Noetherian, to appear. | Zbl 0433.16001

[16] I. Kaplansky, Projective modules. Annals of Math. 68 (1958) 372-377. | MR 100017 | Zbl 0083.25802

[17] J. Mcconnell, Localisation in enveloping rings. J. London Math. Soc. 43 (1968) 421-428; and 3 (1971) 409-410. | MR 228532 | Zbl 0162.05203 | Zbl 0217.33701

[18] B.J. Mueller, Two-sided localisation in Noetherian PI-rings, Ring Theory, Lecture Notes in Pure and Appl. Math. Vol. 51, p.p. 169-190, Marcel Dekker, New York, 1979. | MR 563294 | Zbl 0436.16003

[19] B.J. Mueller, Localization in fully bounded Noetherian rings. Pac. J. Math. 67 (1976) 233-245. | MR 427351 | Zbl 0319.16001 | Zbl 0333.16005

[20] P.F. Smith, Localisation and the AR property. Proc. London Math. Soc. 22 (1971) 39-68. | MR 294383 | Zbl 0208.29703

[21] P.F. Smith, On non-commutative regular local rings, Glasgow Math. J. (1976) 98-102. | MR 422318 | Zbl 0326.16005

[22] R.W. Swan, Algebraic K-Theory. Lecture Notes in Mathematics vol. 76, Springer-Verlag (Berlin) 1968. | MR 245634 | Zbl 0193.34601

[23] P. Tauvel, Sur les quotients premiers de l'algèbre enveloppante d'une algèbre de Lie résoluble. Bull. Soc. Math. France 106 (1978) 177-205. | Numdam | MR 507749 | Zbl 0399.17003

[24] R. Walker, Local rings and normalizing sets of elements. Proc. London Math. Soc. 24 (1972) 27-45. | MR 294399 | Zbl 0224.16004

[25] W. Borho and J.-L. Brylinski, Differential operators on homogeneous spaces I. Inv. Math. 69 (1982) 437-476. | MR 679767 | Zbl 0504.22015

[26] M.-P. Malliavin, Modules sans torsion et modules injectifs sur les algèbres de Lie résolubles, preprint, (1982). | MR 710591 | Zbl 0512.17002

[27] A. Joseph, Towards the Jantzen conjecture III. Comp. Math. 41 (1981) 23-30. | Numdam | MR 594481 | Zbl 0446.17005