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Let $R$ be a commutative ring with identity and let $M$ be a $w$-module over $R$. Denote by $\mathscr{F}_M$ the set of all $w$-submodules of $M$ such that $(M/N)_w$ is $w$-cofinitely generated. Then it is shown that $M$ is $w$-Artinian if and only if $\mathscr{F}_M$ is closed under arbitrary intersections, if and only if $\mathscr{F}_M$ satisfies the descending chain condition.
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참고문헌 (10)
참고문헌 신청
F.W. Anderson / 1992 / Rings and Categories of Modules / SpringerVerlag
C. Faith / 1999 / Rings and Things and a Fine Array of Twentieth Century Associative Algebra / Amer. Math. Soc
J. L. Garc´ıa Hern´andez / 1985 / V-rings relative to Gabriel topologies / Comm. Algebra 13:59~83
J.P. Jans / 1969 / Co-Noetherian rings / J. London Math. Soc 1(1):588~590
A. J. Pena / 1993 / Una caracterizaci´on de los m´odulos Artinianos / Divulg. Mat 1(1):17~24
C. Faith / 1999 / Rings and Things and a Fine Array of Twentieth Century Associative Algebra / Amer. Math. Soc
J. L. Garc´ıa Hern´andez / 1985 / V-rings relative to Gabriel topologies / Comm. Algebra 13:59~83
J.P. Jans / 1969 / Co-Noetherian rings / J. London Math. Soc 1(1):588~590
A. J. Pena / 1993 / Una caracterizaci´on de los m´odulos Artinianos / Divulg. Mat 1(1):17~24
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