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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Ideals containing monics


Authors: Budh Nashier and Warren Nichols
Journal: Proc. Amer. Math. Soc. 99 (1987), 634-636
MSC: Primary 13C10
DOI: https://doi.org/10.1090/S0002-9939-1987-0877030-2
MathSciNet review: 877030
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Abstract: If an ideal $ I$ of $ R[X]$ contains a monic, then every monic in $ I$ modulo $ JR[X]$ ($ J$ being an ideal contained in the Jacobson radical of $ R$) can be lifted to a monic in $ I$. This result is used to give an elementary proof of Horrocks' Theorem.


References [Enhancements On Off] (What's this?)

  • [Bourbaki] N. Bourbaki, Commutative algebra, Addison-Wesley, 1972.
  • [Lam] T. Y. Lam, Serre's Conjecture, Lecture Notes in Math., vol. 635, Springer-Verlag, Berlin and New York, 1978. MR 0485842 (58:5644)
  • [Roitman] Moshe Roitman, On projective modules over polynomial rings, J. Algebra 58 (1979), 51-63. MR 535842 (80g:13004)

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DOI: https://doi.org/10.1090/S0002-9939-1987-0877030-2
Article copyright: © Copyright 1987 American Mathematical Society

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