1992
DOI: 10.4153/cmb-1992-019-3
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Artin Rings with Two-Generated Ideals

Abstract: 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.

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Cited by 2 publications
(1 citation statement)
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“…He also showed that a Noetherian ring R is an n-generated ring (for some n) if and only if there exists a positive integer m such that R M is an m-generated ring for each maximal ideal M of R [Gilmer 1972a;1972b]. For more on n-generated ideals and rings, we refer the readers to [Ameziane Hassani et al 1996;Cohen 1950;Gilmer 1972b;Heinzer and Lantz 1983;Matsuda 1979;McLean 1982;1993;Rush 1991;1992;Sally 1978;Shalev 1986].…”
Section: Introductionmentioning
confidence: 99%
“…He also showed that a Noetherian ring R is an n-generated ring (for some n) if and only if there exists a positive integer m such that R M is an m-generated ring for each maximal ideal M of R [Gilmer 1972a;1972b]. For more on n-generated ideals and rings, we refer the readers to [Ameziane Hassani et al 1996;Cohen 1950;Gilmer 1972b;Heinzer and Lantz 1983;Matsuda 1979;McLean 1982;1993;Rush 1991;1992;Sally 1978;Shalev 1986].…”
Section: Introductionmentioning
confidence: 99%