On the prime submodules of multiplication modules
By R. Ameri. 2003
111 citations recorded by the source corpus.
By considering the notion of multiplication modules over a commutative ring with identity, first we introduce the notion product of two submodules of such modules. Then we use this notion to characterize the prime submodules of a multiplication module. Finally, we state and prove a version of Nakayama lemma for multiplication modules and find some related basic results.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e97912f55235a341dbfe931b331d742ff4286530
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In Algebra and Number Theory
- F. Soheilnia
- Ahmad Yousefian Darani
- Ünsal Teki̇r
- Shahabaddin Ebrahimi Atani
- F. Farzalipour
- H. Ansari-Toroghy
- Faranak Farshadifar
In Geometry and Topology
- F. Soheilnia
- Ahmad Yousefian Darani
- Ünsal Teki̇r
- Shahabaddin Ebrahimi Atani
- F. Farzalipour
- H. Ansari-Toroghy
- Faranak Farshadifar
Citations in the corpus
- On S-prime submodules (2019, background): “The product of K and L is defined as KL = (K :R M)(L :R M)M [2].”
- On weakly prime submodules (2007, background): “Clearly, NK is a submodule of M and NK ⊆ N ∩ K (see [2]).”
- 2-Absorbing and Weakly 2-Absorbing Submodules (2012, background): “Clearly, NK is a submodule of M and NK ⊆ N ∩ K (see [10]).”