Strongly irreducible ideals of a commutative ring |
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| Authors: | William J. Heinzer Louis J. Ratliff Jr. |
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| Affiliation: | a Department of Mathematics, Purdue University, # 1395, West Lafayette, IN 47909-1395, USA
b Department of Mathematics, University of California, Riverside, CA 92521-0135, USA |
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| Abstract: | An ideal I of a ring R is said to be strongly irreducible if for ideals J and K of R, the inclusion J∩K⊆I implies that either J⊆I or K⊆I. The relationship among the families of irreducible ideals, strongly irreducible ideals, and prime ideals of a commutative ring R is considered, and a characterization is given of the Noetherian rings which contain a non-prime strongly irreducible ideal. |
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| Keywords: | 13A15 13C05 13E05 13F99 |
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