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

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

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), 358-383. MR**563234 (81c:16027)****[2]**J.-E. Björk,*Noetherian and Artinian chain conditions of associative rings*, Arch. Math.**24**(1973), 366-379. MR**0344286 (49:9025)****[3]**W. D. Blair,*Right Noetherian rings integral over their centers*, J. Algebra**27**(1973), 187-198. MR**0325679 (48:4026)****[4]**G. Cauchon,*Anneaux premiers, Noetheriens, a identites polynomiales*, Bull. Soc. Math. France**104**(1976), 99-111. MR**0407076 (53:10859)****[5]**P. M. Cohn,*Quadratic extensions of skew fields*, Proc. London Math. Soc.**3**(1951), 531-556. 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), 41-43. MR**0389941 (52:10770)****[8]**J. C. Robson and L. W. Small,*Liberal extensions*, Proc. London Math. Soc.**3(42)**(1981), 87-103. 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,*Non-commutative affine P.I. rings are catenary*, J. Algebra**51**(1978), 12-18. MR**0485980 (58:5772)****[11]**J. T. Stafford,*Non-holonomic modules over Weyl algebras and enveloping algebras*, Invent. Math.**79(3)**(1985), 619-638. MR**782240 (86h:17009)**

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