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Irving, Ronald S.

Primitive ideals of certain Noetherian algebras. (English) Zbl 0403.16015

Math. Z. 169, 77-92 (1979).
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Cited in 3 Documents

MSC:

16P40 Noetherian rings and modules (associative rings and algebras)
16P60 Chain conditions on annihilators and summands: Goldie-type conditions
16P50 Localization and associative Noetherian rings
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16N40 Nil and nilpotent radicals, sets, ideals, associative rings
16S34 Group rings
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
16Gxx Representation theory of associative rings and algebras
16Dxx Modules, bimodules and ideals in associative algebras
16W20 Automorphisms and endomorphisms

Keywords:

Primitive Ideals of Finitely-Generated Noetherian Algebras; Intersection Theorem; Prime Goldie F-Algebra; Finitely-Presented Noetherian Algebra; Separating Set; Baire Property; Primitive Ideal Space; Primitive Ideals of Solvable Enveloping Algebras; Finitely-Generated Nilpotent Group Rings
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\textit{R. S. Irving}, Math. Z. 169, 77--92 (1979; Zbl 0403.16015)
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References:

[1] Dixmer, J.: Algèbres enveloppantes. Paris: Gauthier-Villars 1974
[2] Dixmier, J.: Idéaux primitifs dans les algèbres enveloppantes. J. Algebra48, 96-112 (1977) · Zbl 0366.17007
[3] Duflo, M.: Certaines algèbres de type fini sont des algèbres de Jacobson. J. Algebra27, 358-365 (1973) · Zbl 0279.16010
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[7] Irving, R.: Generic flatness and the Nullstellensatz for Ore extensions. Comm. Algebra7, 259-277 (1979) · Zbl 0402.16002
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[10] Irving, R.: Prime ideals of Ore extensions over commutative rings. II. J. Algebra (to appear) · Zbl 0399.16015
[11] Irving, R.: Some primitive differential operator rings. Math. Z.160, 241-247 (1978) · Zbl 0382.16005
[12] Jacobson, N.: Lectures in abstract algebra. III. Theory of fields and Galois theory. New York, Heidelberg, Berlin: Springer 1976 · Zbl 0322.12001
[13] Jordan, D.: Noetherian Ore extensions and Jacobson rings. J. London Math. Soc. (2)10, 281-291 (1975) · Zbl 0313.16011
[14] Lorenz, M.: Analogs of Clifford’s theorem for polycyclic-by-finite groups. Trans. Amer. Math. Soc. (to appear) · Zbl 0413.16011
[15] Lorenz, M.: Completely prime primitive ideals in group algebras of finitely generated nilpotent-by-finite groups. Comm. Algebra6, 717-734 (1978) · Zbl 0369.16013
[16] Lorenz, M.: Primitive ideals in group algebras of supersoluble groups. Math. Ann.225, 115-122 (1977) · Zbl 0341.16003
[17] Lorenz, M., Passman, D.: Centers and prime ideals in group algebras of polycyclic-by-finite groups. J. Algebra57, 355-386 (1979) · Zbl 0415.16008
[18] Resco, R.: A reduction theorem for the primitivity of tensor products. Preprint · Zbl 0403.16007
[19] Roseblade, J.: Group rings of polycyclic groups. J. Pure Appl. Algebra3, 307-328 (1973) · Zbl 0285.20008
[20] Smith, M.: Private communication
[21] Zalesskii, A.: Irreducible representations of finitely generated nilpotent torsion-free groups. Math. Notes9, 117-123 (1971)
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