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

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Published: Dec 30, 2018
Keywords:
semi normal (pair), $t$-closed (pair), amalgamated algebra
Mathematics Subject Classification:
13F45, 13B10, 13B22.

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Tae In Kwon
Department of Mathematics Changwon National University Changwon 51140, Republic of Korea
Hwankoo Kim
Division of Computer & Information Engineering Hoseo University Asan 31499, Republic of Korea

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.


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Changwon National University

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