A generalization of primary ideals and strongly prime submodules

Afroozeh Jafari ^[1] ; Mohammad Baziar ^[1] ; Saeed Safaeeyan ^[1]
1. [1] Yasouj University
  
  Yasouj University
  
  Irán
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 62, Nº. 2, 2021, págs. 423-432
Idioma: inglés
DOI: 10.33044/revuma.1783
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Resumen
- We present ∗-primary submodules, a generalization of the concept of primary submodules of an R-module. We show that every primary submodule of a Noetherian R-module is ∗-primary. Among other things, we show that over a commutative domain R, every torsion free R-module is ∗-primary. Furthermore, we show that in a cyclic R-module, primary and ∗-primary coincide. Moreover, we give a characterization of ∗-primary submodules for some finitely generated free R-modules.