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Noetherian Tensor Products

Published online by Cambridge University Press:  20 November 2018

E. A. Magarian  and
J. L. Motto
E. A. Magarian
Affiliation:
Stetson University, Deland, FloridaFlorida State University, Tallahassee, Florida
J. L. Motto
Affiliation:
Stetson University, Deland, FloridaFlorida State University, Tallahassee, Florida
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Relatively little is known about the ideal structure of A⊗RA' when A and A' are R-algebras. In [4, p. 460], Curtis and Reiner gave conditions that imply certain tensor products are semi-simple with minimum condition. Herstein considered when the tensor product has zero Jacobson radical in [6, p. 43]. Jacobson [7, p. 114] studied tensor products with no two-sided ideals, and Rosenberg and Zelinsky investigated semi-primary tensor products in [9].

All rings considered in this paper are assumed to be commutative with identity. Furthermore, R will always denote a field.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 2 , June 1972 , pp. 235 - 238
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Bourbaki, N., Algèbre commutative, Ch. 1 and 2 (Fasc. 27) Hermann, Paris, 1961.Google Scholar
2. Bourbaki, N., Algèbre commutative, Ch. 3 and 4 (Fasc. 28) Hermann, Paris, 1961.Google Scholar
3. Bourbaki, N., Algèbre commutative, Ch. 5 and 6 (Fasc. 30) Hermann, Paris, 1964.Google Scholar
4. Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras, Interscience, New York, 1962.Google Scholar
5. Gilmer, R. W. Jr, Contracted ideals with respect to integral extension, Duke Math. J. 34 (1967), 561-572.Google Scholar
6. Herstein, I. N., Theory of rings, Multigraphed lecture notes, Univ. of Chicago Press, Chicago, 1961.Google Scholar
7. Jacobson, N., Structure of rings, Amer. Math. Soc. Colloq. Vol. 37 Amer. Math. Soc, Providence, R.I., 1943.Google Scholar
8. Nagata, M., Local rings, Interscience, New York, 1962.Google Scholar
9. Rosenberg, A. and Zelinsky, D., Tensor products of semiprimary algebras, Duke Math. J., 24 (1957), 555-560.Google Scholar
10. Samuel, P., Algèbre locale, Mémorial des Sciences Mathématique 123, Gauthier-Villas, Paris, 1953.Google Scholar
11. Soublin, J. P., Un anneau cohérent dont Vanneau des polynömes rfest pas cohérent, C. R. Acad. Sci. Paris Ser. A-B, 267 (1968), A241-A243.Google Scholar
12. Zariski, O. and Samuel, P., Commutative algebra, Vol. I, Van Nostrand, Princeton, N.J., 1958.Google Scholar
13. Zariski, O. and Samuel, P., Commutative algebra, Vol. II, Van Nostrand, Princeton, N.J., 1960.Google Scholar
14. Zelinsky, D., Rings with ideal nuclei, Duke Math. J. 18 (1951), 431-442.Google Scholar