On weakly prime submodules

By Shahabaddin Ebrahimi Atani, F. Farzalipour. 2007

85 citations recorded by the source corpus.

Let $ R $ be a commutative ring with non-zero identity. We define a proper submodule $ N $ of an $ R $-module $ M $ to be weakly prime if $ 0\not = rm\in N $( $ r\in R, m\in M $) implies $ m\in N $ or $ rM\subseteq N $. A number of results concerning weakly prime submodules are given. For example, we give three other characterizations of weakly prime submodules.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/22b1e681200798c810499ecc235b9356aba2ce9f

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In Algebra and Number Theory

1. H. Ansari-Toroghy
2. Faranak Farshadifar
3. F. Soheilnia
4. Abdelmalek Azizi
5. Ahmad Yousefian Darani

In Geometry and Topology

1. H. Ansari-Toroghy
2. Faranak Farshadifar
3. F. Soheilnia
4. Abdelmalek Azizi
5. Ahmad Yousefian Darani

Citations in the corpus

• 2-Absorbing and Weakly 2-Absorbing Submodules (2012, methodology): “Weakly prime submodules were introduced by Ebrahimi Atani and Farzalipour in [4].”
• WEAKLY PRIME SUBMODULES AND PRIME SUBMODULES (2006, background): “Weakly prime submodules have been introduced and studied in [5].”
• The Dual Notions of Some Generalizations of Prime Submodules (2011, methodology): “Weakly prime submodules are generalizations of prime submodules and they have been introduced by Behboodi and Koohi in [8].”