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An ideal I of a ring R is called pseudo-irreducible if I cannot be written as an intersection of two comaximal proper ideals of R. In this paper, it is… Click to show full abstract
An ideal I of a ring R is called pseudo-irreducible if I cannot be written as an intersection of two comaximal proper ideals of R. In this paper, it is shown that the maximal spectrum of R is Noetherian if and only if every proper ideal of R can be expressed as a finite intersection of pseudo-irreducible ideals. Using a result of Hochster, we characterize all T1 quasi-compact Noetherian topological spaces.
Keywords:
commutative rings;
ideal;
spectrum noetherian;
rings whose;
characterization commutative
Journal Title: Journal of Algebra and Its Applications
Year Published: 2018
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Journal Title: Journal of Algebra and Its Applications
Year Published: 2018
Link to full text (if available)
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recommendations!