论文标题
正常和坚定不变的变体
Variants of normality and steadfastness deform
论文作者
论文摘要
取消问题询问$ a [x_1，x_2，\ ldots，x_n] \ cong b [y_1，y_2，y_2，\ ldots，y_n] $表示$ a \ cong b $。哈曼（Hamann）将坚定的戒指介绍为戒指，以此为戒指，Abhyankar，Eakin和Heinzer Hold认为取消问题的版本。根据Asanuma，Hamann和Swan的工作，可以以$ p $ seminormelity的特征来表征，这是Swan引入的正常性的一种变体。我们证明，减少Noetherian的本地戒指，$ p $ seminortal and seadfastness变形。我们还证明，在相邻的正式功率系列变量下，$ p $ - 占主导地位和坚定不移是稳定的，以减少（不一定是noetherian）环。我们的方法还提供了新的证据，证明了正常性和弱态性变形的事实，这些事实具有独立的兴趣。
The cancellation problem asks whether $A[X_1,X_2,\ldots,X_n] \cong B[Y_1,Y_2,\ldots,Y_n]$ implies $A \cong B$. Hamann introduced the class of steadfast rings as the rings for which a version of the cancellation problem considered by Abhyankar, Eakin, and Heinzer holds. By work of Asanuma, Hamann, and Swan, steadfastness can be characterized in terms of $p$-seminormality, which is a variant of normality introduced by Swan. We prove that $p$-seminormality and steadfastness deform for reduced Noetherian local rings. We also prove that $p$-seminormality and steadfastness are stable under adjoining formal power series variables for reduced (not necessarily Noetherian) rings. Our methods also give new proofs of the facts that normality and weak normality deform, which are of independent interest.
