Relativez-Ideals in Commutative Rings
| Autor: | F. Azarpanah, Ali Rezaei Aliabad, A. Taherifar |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Communications in Algebra. 41:325-341 |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1080/00927872.2011.630706 |
| Popis: | If I and J are two ideals in a ring R, we call I a zJ-ideal if Ma ∩ J ⊆ I, ∀ a ∈ I, where Ma is the intersection of all maximal ideals containing a. Whenever J ⊈ I and I is a zJ-ideal, we say that I is a relative z-ideal or briefly a rez-ideal, and we call J a z-factor of I. If I is an ideal in a semisimple ring and Ann(I) ≠ (0), we have shown that I is a rez-ideal and the converse is also true for each finitely generated ideal in C(X). Small and large rez-ideals and z-factors are investigated and the largest z-factor of a given semiprime ideal and maximal zJ-ideals for a given ideal J are obtained. Minimal z-factors of a given ideal in a reduced ring are also characterized and it turns out that minimal z-factors of a given ideal I in C(X) are precisely the minimal ideals of C(X) which are not contained in I. Finally, we show that the space X is an F-space if and only if the sum of every rez-ideal and every convex ideal in C(X) is convex, and spaces X for which the intersection of every two semiprime rez-... |
| Databáze: | OpenAIRE |
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