CHARACTERIZATION OF PRIME SUBMODULES OF A FREE MODULE OF FINITE RANK OVER A VALUATION DOMAIN
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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.
Abstract
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.
참고문헌 (10)
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