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Primary rings and tensor products of algebras

Published online by Cambridge University Press:  24 October 2008

L. O'Carroll  and
M. A. Qureshi
L. O'Carroll
Affiliation:
University of Edinburgh
M. A. Qureshi
Affiliation:
University of Edinburgh
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Extract

All rings considered in this paper are non-trivial commutative algebras over a field k; unless indicated otherwise, all tensor products are understood to be taken over k. (Some of the results and concepts extend to general rings, but it is not worth while noting such generalizations.)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 1 , July 1982 , pp. 41 - 48
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

(1)Atiyah, M. F. and Macdonald, I. G.Introduction to commutative algebra (Addison-Wesley, Reading, Mass., 1969).Google Scholar
(2)Burton, D. M.A first course in rings and ideals (Addison-Wesley, Reading, Mass., 1970).Google Scholar
(3)Gilmer, R. W.Multiplicative ideal theory, part II (Queen's University, Kingston, Ontario, 1968).Google Scholar
(4)Kaplansky, I.Commutative rings (University of Chicago Press, 1974).Google Scholar
(5)Matsumura, H.Commutative algebra (Benjamin/Cummings, Reading, Mass., 1980).Google Scholar
(6)Nagata, M.Local rings (John Wiley, New York/London, 1962).Google Scholar
(7)Qureshi, M. A. The transcendental nullstellensatz and allied topics (University of Edinburgh, Ph.D. thesis, 1981).Google Scholar
(8)Seidenbebg, A.The prime ideals of a polynomial ideal under extension of the base field. Ann. Mat. Pura Appl. 102 (1975), 57–59.CrossRefGoogle Scholar
(9)Sharp, R. Y.The effect on associated prime ideals produced by an extension of the base field. Math. Scand. 38 (1976), 43–52.Google Scholar
(10)Sharp, R. Y.Simplifications in the theory of tensor products of field extensions. J. London Math. Soc. (2) 15 (1977), 48–50.CrossRefGoogle Scholar
(11)Sharp, R. Y. and Vámos, P.The dimension of the tensor product of a finite number of field extensions. J. Pure Appl. Algebra 10 (1977), 249–252.Google Scholar
(12)Sweedler, M. E.A units theorem applied to Hopf algebras and Amitsur cohomology. Amer. J. Math. 92 (1970), 259–271.Google Scholar
(13)Vámos, P.On the minimal prime ideals of a tensor product of two fields. Math. Proc. Camb. Phil. Soc. 84 (1978), 25–35.CrossRefGoogle Scholar
(14)Wadsworth, A. R.The Krull dimensions of tensor products of commutative algebras over a field. J. London Math. Soc. (2) 19 (1979), 391–401.Google Scholar
(15)Zariski, O. and Samuel, P.Commutative algebra, vol. I (Springer-Verlag, New York, 1958).Google Scholar
(16)Zariski, O. and Samuel, P.Commutative algebra, vol. II (Springer-Verlag, New York, 1960).Google Scholar