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Let $F=R^{(n)}$ be a free $R$-module of finite rank $n\geq 2$. In this paper, we characterize the prime submodules of $F$ with at most $n$ generators when $R$ is a \pr domain. We also introduce the notion of prime matrix and we show that when $R$ is a valuation domain, every finitely generated prime submodule of $F$ with at least $n$ generators is the row space of a prime matrix.
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참고문헌 (10)
참고문헌 신청
C. P. Lu / 1984 / Prime submodules of modules / Comment. Math. Univ. St. Paul 33 (1) : 61 ~ 69
F. Mirzaei / / On prime submodules of a free module of finite rank over a commutative ring / Comm. Algebra
I. Chiswell / 2001 / Introduction to ∧-trees / World Scientific
M. Behboodi / 2014 / Modules satisfying the prime and maximal radical conditions / J. Commut. Algebra 6 (4) : 505 ~ 524
M. Fontana / 1996 / Prufer Domain / CRC Press
F. Mirzaei / / On prime submodules of a free module of finite rank over a commutative ring / Comm. Algebra
I. Chiswell / 2001 / Introduction to ∧-trees / World Scientific
M. Behboodi / 2014 / Modules satisfying the prime and maximal radical conditions / J. Commut. Algebra 6 (4) : 505 ~ 524
M. Fontana / 1996 / Prufer Domain / CRC Press
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