Annihilator-based dependency relations in modules and radical characterizations

• Date: 2026
• Main Authors: Pekin, Ayten, Özkaya, Hamdullah
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2026
• Subjects: annihilator ideals; radical submodules; dependency relations; coprimary modules; multiplication modules; associated primes; 13C05; 13C13; 13E05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2471
• Journal Title: Algebra and Discrete Mathematics

In this paper we introduce and investigate annihilator based dependency relations for submodules of a unitary left \(R\)-module \(M\) over a commutative Noetherian ring \(R\). We show that two submodules \(N_1, N_2 \leq M\) are radically dependent (in the sense that \(\sqrt{\text{Ann}(N_1+N_2)}=\sqr...