On prime submodules of a finitely generated projective module over a commutative ring
Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 729-741
https://doi.org/10.4134/CKMS.c180332
Published online July 31, 2019
Reza Nekooei, Zahra Pourshafiey
Shahid Bahonar University of Kerman; Shahid Bahonar University of Kerman
Abstract : In this paper we give a full characterization of prime submodules of a finitely generated projective module $M$ over a commutative ring $R$ with identity. Also we study the existence of primary decomposition of a submodule of a finitely generated projective module and characterize the minimal primary decomposition of this submodule. Finally, we characterize the radical of an arbitrary submodule of a finitely generated projective module $M$ and study submodules of $M$ which satisfy the radical formula.
Keywords : projective module, primary decomposition, Dedekind domain, prime submodule, radical of submodule, radical formula
MSC numbers : 13A99, 13C10, 13C99, 13F05
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