On prime submodules of a finitely generated projective module over a commutative ring
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초록
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.
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.
참고문헌 (7)
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- S. Hedayat, "Primary decomposition of submodules of a nitely generated module over a PID", Houston J. Math, 32(2), pp.369~377 (2006)
- T. W. Hungerford, "Algebra" (1980), Springer-Verlag
- F. Mirzaei, "On Prime Submodules of a Finitely Generated Free Module Over a Commutative Ring", Communications in Algebra, 44(9), pp.3966~3975 (2016), Informa UK Limited[DOI]
- F. Mirzaei, "On radical formula and Prufer domains", Bull. Iranian Math. Soc, 42(3), pp.555~563 (2016)
- Dilek Pusat-Yilmaz, "Radicals of submodules of free modules", Communications in Algebra, 27(5), pp.2253~2266 (2007), Informa UK Limited[DOI]