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Let $R\subseteq L \subseteq S$ be ring extensions. Two star operations $\star_{1} \in \st (R, S)$, $\star_{2} \in \st (L, S)$ are said to be linked if whenever $A^{\star_{1}}=R^{\star_{1}}$ for some finitely generated $S$-regular $R$-submodule $A$ of $S$, then $(AL)^{\star_{2}} =L^{\star_{2}}$. We study properties of linked star operations; especially when $\star_{1}$ and $\star_{2}$ are strict star operations. We introduce the notion of Pr\"ufer star multiplication extension (P$\star$ME) and we show that under appropriate conditions, if the extension $R\subseteq S$ is P$\star _{1}$ME and $\star_{1}$ is linked to $\star_{2}$, then $L\subseteq S$ is P$\star _{2}$ME.
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참고문헌 (6)
참고문헌 신청
David E. Dobbs / 1989 / t-Linked overrings and prüfer v-multiplication domains / Communications in Algebra 17(11):2835~2852
Said El Baghdadi / 2005 / w-Divisorial domains / Journal of Algebra 285(1):335~355
John R. Hedstorm / 1980 / Some remarks on star-operations / Journal of Pure and Applied Algebra 18(1):37~44
B.G Kang / 1989 / Prüfer v-multiplication domains and the ring R[X]Nv / Journal of Algebra 123(1):151~170
L. Paudel / 2018 / On the saturations of submodules / Algebra Discrete Math 26(1):110~123
Said El Baghdadi / 2005 / w-Divisorial domains / Journal of Algebra 285(1):335~355
John R. Hedstorm / 1980 / Some remarks on star-operations / Journal of Pure and Applied Algebra 18(1):37~44
B.G Kang / 1989 / Prüfer v-multiplication domains and the ring R[X]Nv / Journal of Algebra 123(1):151~170
L. Paudel / 2018 / On the saturations of submodules / Algebra Discrete Math 26(1):110~123
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