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Let $D$ be an integral domain and $w$ be the so-called $w$-operation on $D$. In this note, we introduce the notion of $*(w)$-domains: $D$ is a $*(w)$-domain if $((\cap (x_i))(\cap (y_j)))_w = \cap (x_iy_j)$ for all nonzero elements $x_1, \dots , x_m; y_1, \dots , y_n$ of $D$. We then show that $D$ is a Pr\"ufer $v$-multiplication domain if and only if $D$ is a $*(w)$-domain and $A^{-1}$ is of finite type for all nonzero finitely generated fractional ideals $A$ of $D$.
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참고문헌 (7)
참고문헌 신청
D.D. Anderson / 2000 / Two star-operations and their induced lattices / Comm. Algebra 28 : 2461 ~ 2475
D.D. Anderson / 2009 / On v-domains and star operations / Comm. Algebra 37 : 3018 ~ 3043
M. Zafrullah / 1986 / On generalized Dedekind domains / Mathematika 33 : 285 ~ 295
M. Zafrullah / 1987 / On a property of pre-Schreier domains / Comm. Algebra 15 : 1895 ~ 1920
M. Zafrullah / 1989 / Ascending chain condition and star operations / Comm. Algebra 17 : 1523 ~ 1533
D.D. Anderson / 2009 / On v-domains and star operations / Comm. Algebra 37 : 3018 ~ 3043
M. Zafrullah / 1986 / On generalized Dedekind domains / Mathematika 33 : 285 ~ 295
M. Zafrullah / 1987 / On a property of pre-Schreier domains / Comm. Algebra 15 : 1895 ~ 1920
M. Zafrullah / 1989 / Ascending chain condition and star operations / Comm. Algebra 17 : 1523 ~ 1533
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