Generic Flatness and the Jacobson Conjecture

REFERENCES

• Artin , M. , Small , L. W. , Zhang , J. J. ( 1999 ). Generic flatness for strongly Noetherian algebras . J. Algebra 221 : 579 – 610 . [CSA]
   Web of Science ®Google Scholar
• Chatters , A. W. , Hajarnavis , C. R. ( 1980 ). Rings with Chain Conditions . Boston : Pitman Advanced Publishing Program .
   Google Scholar
• Cortzen , B. , Small , L. W. (1988). Finite extensions of rings. Proc. Amer. Math. Soc. 103(4):1085–1062. [CSA]
   Google Scholar
• Eisenbud , D. ( 1995 ). Commutative Algebra with a View Toward Algebraic Geometry . New York : Springer-Verlag .
   Google Scholar
• Goldman , O. ( 1951 ). Hilbert rings and the hilbert nullstellensatz . Math. Z. 54 : 136 – 140 . [CSA] [CROSSREF]
   Google Scholar
• Goodearl , K. R. , Letzter , E. S. ( 1995 ). Skew polynomial extensions of commutative Noetherian Jacobson rings . Proc. Amer. Math. Soc. 123 : 1673 – 1679 . [CSA]
   Google Scholar
• Goodearl , K. R. , Warfield , R. B. Jr. ( 1989 ). An Introduction to Noncommutative Noetherian Rings . Cambridge : Cambridge University Press .
   Google Scholar
• Herstein , I. N. ( 1965 ). A counterexample in Noetherian rings . Proc. N.A.S. 54 : 1036 – 1037 . [CSA]
   PubMedGoogle Scholar
• Jacobson , N. ( 1945 ). The radical and semi-simplicity for arbitrary rings . Am. J. Math. 67 : 300 – 320 . [CSA]
   Web of Science ®Google Scholar
• Jategoankar , A. V. ( 1968 ). Left principal ideal domains . J. Algebra 8 : 148 – 155 . [CSA] [CROSSREF]
   Google Scholar
• Jategaonkar , A. V. ( 1969 ). A counter-example in ring theory and homological algebra . J. Algebra 12 : 418 – 440 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Jategoankar , A. V. ( 1974 ). Relative krull dimension and prime ideals in right Noetherian rings . Comm. Algebra 2 : 429 – 468 . [CSA]
   Google Scholar
• Kaplansky , I. ( 1970 ). Commutative Rings . Boston : Allyn and Bacon .
   Google Scholar
• Krull , W. ( 1951 ). Jacobsonsche ringe, hilbertscher nullstellensatz, dimensionstheorie . Math. Z. 54 : 354 – 387 . [CSA] [CROSSREF]
   Google Scholar
• Lam , T. Y. ( 1995 ). Exercises in Classical Ring Theory . New York : Springer-Verlag .
   Google Scholar
• McConnell , J. C. ( 1990 ). Quantum groups, filtered rings, and Gel'fand-Kirillov dimension . Noncommutative Ring Theory (Athens, OH, 1989) . Lecture Notes in Math., 1448 . Berlin : Springer , pp. 139 – 147 .
   Google Scholar
• McConnell , J. C. , Robson , J. C. ( 1987 ). Noncommutative Noetherian Rings . Chichester : John Wiley & Sons .
   Google Scholar
• Quillen , D. ( 1969 ). On the endomorphism ring of a simple module over an enveloping algebra . Proc. Amer. Math. Soc. 21 : 171 – 172 . [CSA]
   Web of Science ®Google Scholar
• Rowen , L. H. ( 1980 ). Polynomial Identities in Ring Theory . New York : Academic Press .
   Google Scholar
• Stafford , J. T. , Zhang , J. J. ( 2003 ). Algebras without Noetherian filtrations . Proc. Amer. Math. Soc. 131 : 1329 – 1338 . [CSA] [CROSSREF]
   Google Scholar
• Stephenson , D. R. , Zhang , J. J. ( 1997 ). Growth of graded Noetherian rings . Proc. Amer. Math. Soc. 125 : 1983 – 1605 . [CSA] [CROSSREF]
   Google Scholar
• Watters , J. F. ( 1975 ). Polynomial extensions of Jacobson rings . J. Algebra 36 : 302 – 308 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Yekutieli , A. , Zhang , J. J. ( 1999 ). Rings with auslander dualizing complexes . J. Algebra 213 : 1 – 51 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Communicated by E. Zelmanov.
   Google Scholar