Academic Journal
Almost radicalization and almost radical ideal.
| Τίτλος: | Almost radicalization and almost radical ideal. |
|---|---|
| Συγγραφείς: | Abouhalaka, Alaa1 (AUTHOR) alaa1aclids@gmail.com |
| Πηγή: | Journal of Algebra & Its Applications. Sep2026, Vol. 25 Issue 11, p1-12. 12p. |
| Θεματικοί όροι: | *Ideals (Algebra), *Prime ideals, *Ring theory |
| Περίληψη: | An ideal P of a ring R is called almost prime ideal if A B ⊆ P and A B ⊈ P 2 implies either A ⊆ P or B ⊆ P , for any ideals A , B of R. Here, we introduce the concept of almost m -system, in order to be able to define the almost prime radical of an ideal, also we give an equivalent definition showing that the almost prime radical of an ideal I , if it exists, is the intersection of all the (minimal) almost prime ideals P such that I ⊆ P , I 2 = P 2 . We also provide many of interesting properties. In addition, we examine the almost prime radicals of important ideals, such as the prime radical ideal Nil ∗ (R) , and Nil ∗ (R) -ideal. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
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