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- Title
RINGS WITH DIVISIBILITY ON ASCENDING CHAINS OF IDEALS.
- Authors
Es safi, Oussama Aymane; Mahdou, Najib; Yousif, Mohamed
- Abstract
According to Dastanpour and Ghorbani, a ring R is said to satisfy divisibility on ascending chains of right ideals (ACCd) if, for every ascending chain of right ideals I1 ⊆ I2 ⊆ I3 ⊆ I4 ⊆ ... of R, there exists an integer k ∈ N such that for each i ≥ k, there exists an element ai ∈ R such that Ii = aiIi+1. In this paper, we examine the transfer of the ACCd-condition on ideals to trivial ring extensions. Moreover, we investigate the connection between the ACCd on ideals and other ascending chain conditions. For example we will prove that if R is a ring with ACCd on ideals, then R has ACC on prime ideals.
- Subjects
PRIME ideals; NOETHERIAN rings; COMMUTATIVE rings; DIVISIBILITY groups; INTEGERS
- Publication
International Electronic Journal of Algebra, 2024, Vol 35, p82
- ISSN
1306-6048
- Publication type
Article
- DOI
10.24330/ieja.1299720