A homological characterization of Krull domains
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초록
Let $R$ be a commutative ring. In this paper, the $w$-projective Basis Lemma for $w$-projective modules is given. Then it is shown that for a domain, nonzero $w$-projective ideals and nonzero $w$-invertible ideals coincide. As an application, it is proved that $R$ is a Krull domain if and only if every submodule of finitely generated projective modules is $w$-projective.
Abstract
Let $R$ be a commutative ring. In this paper, the $w$-projective Basis Lemma for $w$-projective modules is given. Then it is shown that for a domain, nonzero $w$-projective ideals and nonzero $w$-invertible ideals coincide. As an application, it is proved that $R$ is a Krull domain if and only if every submodule of finitely generated projective modules is $w$-projective.
참고문헌 (9)
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