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Excellent Extension and Comparability of Regular Rings

Volume 10, Number 2 (2010), 1 - 6

Excellent Extension and Comparability of Regular Rings

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Abstract

Let $S$ be an excellent extension of a (von Neumann) regular ring $R$. In this note, we study comparability of $S$ related to comparability of $R$. We show that if $R$ has the $n$-unperforation property, then $R$ satisfies $s$-comparability, almost comparability or weak comparability if and only if so does $S$.