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A generalization of primary ideals and strongly prime submodules
Volume 62, no. 2
(2021),
pp. 423–432
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 by the Unión Matemática Argentina |
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