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    Bavula, V. V. 2008. Finite Generation of the Group of Eigenvalues for Sets of Derivations or Automorphisms of Division Algebras. Communications in Algebra, Vol. 36, Issue. 6, p. 2195.


    Bell, Jason Farina, John and Pendergrass-Rice, Cayley 2008. Stably just infinite rings. Journal of Algebra, Vol. 319, Issue. 6, p. 2533.


    Bell, Jason P. 2007. Noetherian algebras over algebraically closed fields. Journal of Algebra, Vol. 310, Issue. 1, p. 148.


    Bouchiba, S. and Kabbaj, S. 2002. Tensor products of Cohen–Macaulay rings: solution to a problem of Grothendieck. Journal of Algebra, Vol. 252, Issue. 1, p. 65.


    Bouchiba, Samir E. Dobbs, David and Kabbaj, Salah-Eddine 2002. On the prime ideal structure of tensor products of algebras. Journal of Pure and Applied Algebra, Vol. 176, Issue. 2-3, p. 89.


    Keun Koo, Hyeng 1990. The injectivity of a division ring D as a left D⊗kDop-module∗. Communications in Algebra, Vol. 18, Issue. 2, p. 453.


    Bowman, S. R. and O’Carroll, L. 1986. Tensor products and localizations of algebras. Nagoya Mathematical Journal, Vol. 102, p. 155.


    Sigurdsson, Gunnar 1984. Differential operator rings whose prime factors have bounded Goldie dimension. Archiv der Mathematik, Vol. 42, Issue. 4, p. 348.


    O'Carroll, L. and Qureshi, M. A. 1982. Primary rings and tensor products of algebras. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 92, Issue. 01, p. 41.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 84, Issue 1
  • July 1978, pp. 25-35

On the minimal prime ideals of a tensor product of two fields

  • P. Vámos (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100054840
  • Published online: 24 October 2008
Abstract

Let F be a field, L a commutative F-algebra and K an extension field of F. An important area of commutative algebra is the study of the passage from L to the k-algebra KFL, i.e. the investigation of the behaviour of the ideals of L under ‘extension of scalars’. In most problems of this kind one finds that the problem is reduced to the case when the algebra L is itself an extension field of F. It is for this reason that tensor products of fields play an important role (see, for example, (2), chap, viii, (3), (5), (9) and (12), vol. I).

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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