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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.
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참고문헌 (9)
참고문헌 신청
D. D. Anderson / 2000 / Two star-operations and their induced lattices / Comm. Algebra 28(5):2461~2475
S. E. Baghdadi / 2016 / Divisible is injective over Krull domains / Comm. Algebra 44:4294~4301
L. Fuchs / 2001 / Modules over non-Noetherian domains, Math. Surveys and Monographs 84
B. G. Kang / 1989 / On the converse of a well-known theorem about Krull domains / J. Algebra 124:284~299
M. Nishi / 1975 / Codivisorial and divisorial modules over completely integrally closed domains (I) / Hiroshima Math. J. 5(2):269~292
S. E. Baghdadi / 2016 / Divisible is injective over Krull domains / Comm. Algebra 44:4294~4301
L. Fuchs / 2001 / Modules over non-Noetherian domains, Math. Surveys and Monographs 84
B. G. Kang / 1989 / On the converse of a well-known theorem about Krull domains / J. Algebra 124:284~299
M. Nishi / 1975 / Codivisorial and divisorial modules over completely integrally closed domains (I) / Hiroshima Math. J. 5(2):269~292
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