| Περίληψη: |
A proper ideal I in a ring R is called strongly irreducible (briefly, SI-ideal), if J ∩ K ⊆ I then J ⊆ I or K ⊆ I , where J , K are ideals of R. We show that whenever in a local Noetherian duo domain, a power of its maximal ideal, M say, is principal, then so is M. It is also shown that whenever I is an SI-ideal in a Noetherian duo ring R where I = P and I ≠ P with ht (P) > 0 , then R P is a domain. Finally in a Noetherian duo ring R , non-prime ideals with positive heights, which are SI-ideal, are characterized. [ABSTRACT FROM AUTHOR] |