Finite extensions of rings

Authors:
Barbara Cortzen and Lance W. Small

Journal:
Proc. Amer. Math. Soc. **103** (1988), 1058-1062

MSC:
Primary 16A38; Secondary 16A21, 16A33, 16A56

MathSciNet review:
954983

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**S. A. Amitsur and L. W. Small,*Prime ideals in PI rings*, J. Algebra**62**(1980), no. 2, 358–383. MR**563234**, 10.1016/0021-8693(80)90188-X**[2]**Jan-Erik Björk,*Noetherian and Artinian chain conditions of associative rings*, Arch. Math. (Basel)**24**(1973), 366–378. MR**0344286****[3]**William D. Blair,*Right Noetherian rings integral over their centers*, J. Algebra**27**(1973), 187–198. MR**0325679****[4]**Gérard Cauchon,*Anneaux semi-premiers, noethériens, à identités polynômiales*, Bull. Soc. Math. France**104**(1976), no. 1, 99–111. MR**0407076****[5]**P. M. Cohn,*Quadratic extensions of skew fields*, Proc. London Math. Soc. (3)**11**(1961), 531–556. MR**0136633****[6]**Robert Gordon and J. C. Robson,*Krull dimension*, American Mathematical Society, Providence, R.I., 1973. Memoirs of the American Mathematical Society, No. 133. MR**0352177****[7]**I. N. Herstein and Lance W. Small,*An extension of a theorem of Schur*, Linear and Multilinear Algebra**3**(1975/76), no. 1/2, 41–43. Collection of articles dedicated to Olga Taussky-Todd. MR**0389941****[8]**J. C. Robson and Lance W. Small,*Liberal extensions*, Proc. London Math. Soc. (3)**42**(1981), no. 1, 87–103. MR**602124**, 10.1112/plms/s3-42.1.87**[9]**Louis Halle Rowen,*Polynomial identities in ring theory*, Pure and Applied Mathematics, vol. 84, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. MR**576061****[10]**William Schelter,*Non-commutative affine P.I. rings are catenary*, J. Algebra**51**(1978), no. 1, 12–18. MR**0485980****[11]**J. T. Stafford,*Nonholonomic modules over Weyl algebras and enveloping algebras*, Invent. Math.**79**(1985), no. 3, 619–638. MR**782240**, 10.1007/BF01388528

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
16A38,
16A21,
16A33,
16A56

Retrieve articles in all journals with MSC: 16A38, 16A21, 16A33, 16A56

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0954983-6

Article copyright:
© Copyright 1988
American Mathematical Society