Finite extensions of rings
Authors:
Barbara Cortzen and Lance W. Small
Journal:
Proc. Amer. Math. Soc. 103 (1988), 10581062
MSC:
Primary 16A38; Secondary 16A21, 16A33, 16A56
MathSciNet review:
954983
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Abstract: The paper concerns some cases of ring extensions , where is finitely generated as a right module and is right Noetherian. In it is shown that if is a Jacobson ring, then so is , with the converse true in the case. In we show that if is semiprime , must also be left (as well as right) Noetherian and is finitely generated as a left .module. contains a result on rings.
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 [1]
 S. A. Amitsur and L. W. Small, Prime ideals in PIrings, J. Algebra 62 (1980), 358383. MR 563234 (81c:16027)
 [2]
 J.E. Björk, Noetherian and Artinian chain conditions of associative rings, Arch. Math. 24 (1973), 366379. MR 0344286 (49:9025)
 [3]
 W. D. Blair, Right Noetherian rings integral over their centers, J. Algebra 27 (1973), 187198. MR 0325679 (48:4026)
 [4]
 G. Cauchon, Anneaux premiers, Noetheriens, a identites polynomiales, Bull. Soc. Math. France 104 (1976), 99111. MR 0407076 (53:10859)
 [5]
 P. M. Cohn, Quadratic extensions of skew fields, Proc. London Math. Soc. 3 (1951), 531556. MR 0136633 (25:101)
 [6]
 R. Gordon and J. C. Robson, Krull dimension, Mem. Amer. Math. Soc., no. 133, 1973. MR 0352177 (50:4664)
 [7]
 I. N. Herstein and L. W. Small, An extension of a theorem of Schur, Linear and Multilinear Algebra 3 (1975), 4143. MR 0389941 (52:10770)
 [8]
 J. C. Robson and L. W. Small, Liberal extensions, Proc. London Math. Soc. 3(42) (1981), 87103. MR 602124 (82c:16025)
 [9]
 L. H. Rowen, Polynomial identities in ring theory, Academic Press, New York, 1980. MR 576061 (82a:16021)
 [10]
 W. Schelter, Noncommutative affine P.I. rings are catenary, J. Algebra 51 (1978), 1218. MR 0485980 (58:5772)
 [11]
 J. T. Stafford, Nonholonomic modules over Weyl algebras and enveloping algebras, Invent. Math. 79(3) (1985), 619638. MR 782240 (86h:17009)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198809549836
PII:
S 00029939(1988)09549836
Article copyright:
© Copyright 1988
American Mathematical Society
