论文标题
欧姆 - 拉什代数的麦考伊物业
The McCoy property in Ohm-Rush algebras
论文作者
论文摘要
ohm-rush代数$ r \ rightarrow s $被称为 * mccoy *，如果对于任何零迪多级$ f $ in $ s $，其内容$ c（f）$在$ r $中具有非零的歼灭器，因为McCoy在$ s = r [x] $时证明了这一点。我们通过忠实的ohm-rush代数和麦考伊的财产并不是弱内容代数来回答Nasehpour的问题。但是，我们表明，忠实的欧姆 - 拉什代数是一个弱的内容代数iff $ r/i \ rightarrow s/i s $是所有激进的（resp。prime）理想的$ i $ r $的麦科伊。当$ r $是noetherian（或具有更通用的\ emph {fidel（a）}属性）时，我们表明$ r/i \ rightarrow s/is $ $ is $ is McCoy是所有理想的。
An Ohm-Rush algebra $R \rightarrow S$ is called *McCoy* if for any zero-divisor $f$ in $S$, its content $c(f)$ has nonzero annihilator in $R$, because McCoy proved this when $S=R[x]$. We answer a question of Nasehpour by giving an example of a faithfully flat Ohm-Rush algebra with the McCoy property that is not a weak content algebra. However, we show that a faithfully flat Ohm-Rush algebra is a weak content algebra iff $R/I \rightarrow S/I S$ is McCoy for all radical (resp. prime) ideals $I$ of $R$. When $R$ is Noetherian (or has the more general \emph{fidel (A)} property), we show that it is equivalent that $R/I \rightarrow S/IS$ is McCoy for all ideals.
