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Artin Rings with Two-Generated Ideals

Published online by Cambridge University Press:  20 November 2018

David E. Rush
David E. Rush*
Affiliation:
Department of Mathematics University of California at Riverside Riverside, California 92521-0135
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Abstract

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It is shown that each commutative Artin local ring having each of its ideals generated by two elements is the homomorphic image of a one-dimensional local complete intersection ring which also has each of its ideals generated by two elements. It is indicated how this can be applied to show that the property that each ideal is projective over its endomorphism ring does not pass to homomorphic images, and in determining the commutative group rings with the two-generator property.

Keywords

13A1513H1013F99.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 1 , 01 March 1992 , pp. 133 - 135
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Bass, H., On the ubiquity ofGorenstein rings, Math. Z., 82(1963),8–28.Google Scholar
2. Cohen, I. S., On the structure and ideal theory of complete local rings, Trans. Amer. Math. Soc. 59(1946) 54–106.Google Scholar
3. Greither, C., On the two generator problem for ideals of a one-dimensional ring J. Pure Appl. Algebra, 24 (1982) 265–276.Google Scholar
4. Thomas Hungerford, W., On the structure of principal ideal rings, Pacific J. Math. 25 (1968) 543–547.Google Scholar
5. Kunz, E., Introduction to Commutative Algebra and Algebraic Geometry, Birkhauser, Boston, 1985.Google Scholar
6. Matlis, E., The two generator problem for ideals, Mich. Math. J., 17(1970) 257–265.Google Scholar
7. McLean, K. R., Local rings with bounded ideals, J. Algebra, 74(1982) 328–332.Google Scholar
8. Okon, J. S., Rush, D. E. and Vicknair, J. P., Commutative semigroup rings with two-generated ideals, J. London Math. Soc, to appear.Google Scholar
9. Okon, J. S. and Vicknair, J. P., Artinian group rings with two-generated ideals, Communications in Alg., to appear.Google Scholar
10. Rush, D. E., Rings with two-generated ideals, J. Pure Appl. Algebra, 73(1991),257–275.Google Scholar
11. Sally, J. D. and W V. Wasconcclos, Stable rings and a problem of Bass, Bull. Amer. Soc, 79(1973) 574–576.Google Scholar
12. Sally, J. D., Stable rings, J. Pure Appl. Algebra, 4(1974) 319–336.Google Scholar