论文标题
指数理想和无效的
Exponential ideals and a Nullstellensatz
论文作者
论文摘要
我们证明了用于部分指数字段$（k，e）$的nullstellensatz的版本，即使指数多项式$ k [x_1，\ ldots，x_n]^e $不是希尔伯特环。我们表明，在某些自然条件下，人们可以将$ k [x_1，\ ldots，x_n]^e $的理想嵌入到指数理想中。如果理想由指数多项式和指数函数的一个迭代组成，我们表明可以满足这些条件。我们将结果应用于有序指数字段的情况。
We prove a version of a Nullstellensatz for partial exponential fields $(K,E)$, even though the ring of exponential polynomials $K[X_1,\ldots,X_n]^E$ is not a Hilbert ring. We show that under certain natural conditions one can embed an ideal of $K[X_1,\ldots,X_n]^E$ into an exponential ideal. In case the ideal consists of exponential polynomials with one iteration of the exponential function, we show that these conditions can be met. We apply our results to the case of ordered exponential fields.
