n-Absorbing Ideals of Commutative Rings and Recent Progress on Three Conjectures: A Survey
Let R be a commutative ring with 1 ≠ 0. Recall that a proper ideal I of R is called a 2-absorbing ideal of R if a,b,c ∈ R and abc ∈ I, then ab ∈ I or ac ∈ I or bc ∈ I . A more general concept than 2-absorbing ideals is the concept of n-absorbing ideals. Let n ≥ 1 be a positive integer. A proper idea...
محفوظ في:
| المؤلف الرئيسي: | |
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| التنسيق: | bookPart |
| منشور في: |
2017
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/25074 |
| الوسوم: |
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| الملخص: | Let R be a commutative ring with 1 ≠ 0. Recall that a proper ideal I of R is called a 2-absorbing ideal of R if a,b,c ∈ R and abc ∈ I, then ab ∈ I or ac ∈ I or bc ∈ I . A more general concept than 2-absorbing ideals is the concept of n-absorbing ideals. Let n ≥ 1 be a positive integer. A proper ideal I of R is called an n-absorbing ideal of R if a1,a2,…an+1 ∈ R and a1a2…an+1 ∈ I, then there are n of the ai's whose product is in I. The concept of n-absorbing ideals is a generalization of the concept of prime ideals (note that a prime ideal of R is a 1-absorbing ideal of R). In this survey article, we collect some old and recent results on n-absorbing ideals of commutative rings. |
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