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Primitivity in differential operator rings. (English) Zbl 0495.16002

MSC:
16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras)
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16W20 Automorphisms and endomorphisms
16D30 Infinite-dimensional simple rings (except as in 16Kxx)
16P40 Noetherian rings and modules (associative rings and algebras)
13N05 Modules of differentials
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References:
[1] Amitsur, S.A.: A generalization of a theorem on linear differential equations. Bull. Amer. Math. Soc.54, 937-941 (1948) · Zbl 0034.19803 · doi:10.1090/S0002-9904-1948-09102-9
[2] Amitsur, S.A.: Derivations in simple rings. Proc. London Math. Soc. (3)7, 87-112 (1957) · Zbl 0083.02803 · doi:10.1112/plms/s3-7.1.87
[3] Carlson, R.C., Goodearl, K.R.: Commutants of ordinary differential operators. J. Differential Equations35, 339-365 (1980) · Zbl 0418.34021 · doi:10.1016/0022-0396(80)90033-9
[4] Cozzens, J.H., Faith, C.: Simple Noetherian Rings. Cambridge: Cambridge University Press 1975 · Zbl 0314.16001
[5] Dixmier, J.: Enveloping Algebras. Amsterdam: North-Holland 1977 · Zbl 0346.17010
[6] Goodearl, K.R.: Global dimension of differential operator rings III. J. London Math. Soc. (2)17, 397-409 (1978) · Zbl 0389.16015 · doi:10.1112/jlms/s2-17.3.397
[7] Hart, R.: Krull dimension and global dimension of simple Ore-extensions. Math. Z.121, 341-345 (1971) · Zbl 0212.05801 · doi:10.1007/BF01109980
[8] Jacobson, N.: Pseudo-linear transformations. Ann. of Math. (2)38, 484-507 (1937) · JFM 63.0087.01 · doi:10.2307/1968565
[9] Jordan, D.A.: Noetherian Ore extensions and Jacobson rings. J. London Math. Soc. (2)10, 281-291 (1975) · Zbl 0313.16011 · doi:10.1112/jlms/s2-10.3.281
[10] Jordan, D.A.: Primitive Ore extensions. Glasgow Math. J.18, 93-97 (1977) · Zbl 0347.16020 · doi:10.1017/S0017089500003086
[11] McConnell, J.C.: Representations of solvable Lie algebras V: On the Gelfand-Kirillov dimension of simple modules. Preprint · Zbl 0484.16013
[12] McCoy, N.H.: Prime ideals in general rings. Amer. J. Math.71, 823-833 (1949) · Zbl 0035.01804 · doi:10.2307/2372366
[13] Procesi, C.: Rings with Polynomial Identities. New York: Dekker 1973 · Zbl 0262.16018
[14] Seidenberg, A.: Differential ideals in rings of finitely generated type. Amer. J. Math.89, 22-42 (1967) · Zbl 0152.02905 · doi:10.2307/2373093
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