Revista de la
Unión Matemática Argentina
A generalization of primary ideals and strongly prime submodules
Afroozeh Jafari, Mohammad Baziar, and Saeed Safaeeyan
Volume 62, no. 2 (2021), pp. 423–432

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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.