Generalized normality in ring extensions involving amalgamated algebras
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In this paper, seminormality and $t$-closedness in ring extensions involving amalgamated algebras are studied. Let $R \subseteq T$ be a ring extension with ideals $I \subseteq J$, respectively such that $J$ is contained in the conductor of $R$ in $T$. Assume that $T$ is integral over $R$. Then it is shown that $(R \bowtie I, T \bowtie J)$ is a seminormal (resp., $t$-closed) pair if and only if $(R, T)$ is a seminormal (resp., $t$-closed) pair.
Abstract
In this paper, seminormality and $t$-closedness in ring extensions involving amalgamated algebras are studied. Let $R \subseteq T$ be a ring extension with ideals $I \subseteq J$, respectively such that $J$ is contained in the conductor of $R$ in $T$. Assume that $T$ is integral over $R$. Then it is shown that $(R \bowtie I, T \bowtie J)$ is a seminormal (resp., $t$-closed) pair if and only if $(R, T)$ is a seminormal (resp., $t$-closed) pair.
참고문헌 (11)
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