[HTML][HTML] Strongly irreducible ideals of a commutative ring
WJ Heinzer, LJ Ratliff Jr, DE Rush - Journal of Pure and Applied Algebra, 2002 - Elsevier
WJ Heinzer, LJ Ratliff Jr, DE Rush
Journal of Pure and Applied Algebra, 2002•ElsevierAn 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.
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.
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.
Elsevier
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