论文标题
数量代数
Amount algebras
论文作者
论文摘要
在本文中，作为对内容代数的概括，我们引入了代数数量。与Anderson-Badawi $ω_{r [x]}（i [x]）=ω_r（i）$构想相似，我们在某些情况下证明，公式$ω_b（i^ε）=ω_r（i^ω_r（i）$ holds以某种数量$ r $ r $ r $ r $ r $ r $ r $ r $ r $ is $ is $ i是$ i $ i $ i $ r. $ n $是理想的$ i $ $ r $是$ n $ - 吸收。上述公式的推论是，例如，如果$ r $是prüfer域或无扭转的估值环，而$ i $是$ r $的根本理想，则是$ω__________________[x] [x]}（i [x]}（i [[x]]）=ω_r（i）$。
In this paper, as a generalization to content algebras, we introduce amount algebras. Similar to the Anderson-Badawi $ω_{R[X]}(I[X])=ω_R(I)$ conjecture, we prove that under some conditions, the formula $ω_B(I^ε)=ω_R(I)$ holds for some amount $R$-algebras $B$ and some ideals $I$ of $R$, where $ω_R(I)$ is the smallest positive integer $n$ that the ideal $I$ of $R$ is $n$-absorbing. A corollary to the mentioned formula is that if, for example, $R$ is a Prüfer domain or a torsion-free valuation ring and $I$ is a radical ideal of $R$, then $ω_{R[][X]]}(I[[X]])=ω_R(I)$.
