Korean J. Math.  Vol 26, No 4 (2018)  pp.701-708
DOI: https://doi.org/10.11568/kjm.2018.26.4.701

Generalized normality in ring extensions involving amalgamated algebras

Tae In Kwon, Hwankoo Kim

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.

Keywords


semi normal (pair); $t$-closed (pair); amalgamated algebra

Subject classification

13F45, 13B10, 13B22.

Sponsor(s)

Changwon National University

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References


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