论文标题
功能程度和算术应用，I：功能度的集合
Functional Degrees And Arithmetic Applications, I: The Set Of Functional Degrees
论文作者
论文摘要
我们进一步开发了交换组之间地图功能程度的Aichinger-Moosbauer计算。对于任何固定的给定的交换组$ a $ a和$ b $，我们计算了地图$ f：a \ longrightarrow b $可以拥有的最大可能的有限功能学位。我们还确定了此类地图的所有可能程度的集合。 This also yields a solution to Aichinger and Moosbauer's problem of finding the nilpotency index of the augmentation ideal of group rings of the form $Z_{p^β}[Z_{p^{α_1}}\times Z_{p^{α_2}}\times\dotsm\times Z_{p^{α_n}}]$ with $ p，β，n，α_1，\ dotsc，α_n\ in \ mathbb {z}^+$，$ p $ prime。
We give a further development of the Aichinger-Moosbauer calculus of functional degrees of maps between commutative groups. For any fixed given commutative groups $A$ and $B$, we compute the largest possible finite functional degree that a map $f: A \longrightarrow B$ can have. We also determine the set of all possible degrees of such maps. This also yields a solution to Aichinger and Moosbauer's problem of finding the nilpotency index of the augmentation ideal of group rings of the form $Z_{p^β}[Z_{p^{α_1}}\times Z_{p^{α_2}}\times\dotsm\times Z_{p^{α_n}}]$ with $p,β,n,α_1,\dotsc,α_n\in\mathbb{Z}^+$, $p$ prime.
