A generalization of primary ideals and strongly prime submodules

Authors

  • Afroozeh Jafari Department of Mathematics, Yasouj University, Yasouj, 75914, Iran
  • Mohammad Baziar Department of Mathematics, Yasouj University, Yasouj, 75914, Iran
  • Saeed Safaeeyan Department of Mathematics, Yasouj University, Yasouj, 75914, Iran

DOI:

https://doi.org/10.33044/revuma.1783

Abstract

 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.

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Published

2021-12-03

Issue

Vol. 62 No. 2 (2021)

Section

Article

License

Copyright (c) 2022 Afroozeh Jafari, Mohammad Baziar, Saeed Safaeeyan

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