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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.
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참고문헌 (7)
참고문헌 신청
Mustafa Alkan / 2006 / Projective modules and prime submodules / Czechoslovak Mathematical Journal 56(2):601~611
S. Hedayat / 2005 / Characterization of prime submodules of a nitely generated free module over a PID / Houston J. Math 31(1):75~85
S. Hedayat / 2006 / Primary decomposition of submodules of a nitely generated module over a PID / Houston J. Math 32(2):369~377
T. W. Hungerford / 1980 / Algebra / Springer-Verlag
F. Mirzaei / 2016 / On Prime Submodules of a Finitely Generated Free Module Over a Commutative Ring / Communications in Algebra 44(9):3966~3975
S. Hedayat / 2005 / Characterization of prime submodules of a nitely generated free module over a PID / Houston J. Math 31(1):75~85
S. Hedayat / 2006 / Primary decomposition of submodules of a nitely generated module over a PID / Houston J. Math 32(2):369~377
T. W. Hungerford / 1980 / Algebra / Springer-Verlag
F. Mirzaei / 2016 / On Prime Submodules of a Finitely Generated Free Module Over a Commutative Ring / Communications in Algebra 44(9):3966~3975
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