论文标题
指数多项式环中的电子思想
E-ideals in exponential polynomial ring
论文作者
论文摘要
我们在指数式字段的指数多项式环的背景下研究了指数理想。我们为指数理想建立了两个不同的最大概念，并探索了它们与灵巧性的关系。 与经典方案相比，这三个概念 - 敏锐，最大和电子最佳 - 最大程度 - 是独立的。此外，我们证明，在代数封闭的场K上，$ k^n $的点与指数多项式环的最大指数理想之间的对应关系分解。最后，我们介绍并表征了指数激进的理想。 我们研究了指数多数环中的指数理想。我们研究了指数级理想的两个最大概念，并将其与灵巧性联系起来。这三个概念是独立的，与经典案例不同。我们还表明，在代数封闭的场k上，k^n点和指数多项式环的最大理想之间的对应关系不存在。
We investigate exponential ideals within the context of exponential polynomial rings over exponential fields. We establish two distinct notions of maximality for exponential ideals and explore their relationship to primeness. These three concepts--prime, maximal, and E-maximal--are shown to be independent, in contrast to the classical scenario. Furthermore, we demonstrate that, over an algebraically closed field K, the correspondence between points of $K^n$ and maximal exponential ideals of the ring of exponential polynomials breaks down. Finally, we introduce and characterize exponential radical ideals. We investigate exponential ideals in the exponential polynomial ring over an exponential field. We study two notions of maximality for exponential ideals, and relate them to primeness. These three notions are independent, unlike in the classical case. We also show that over an algebraically closed field K the correspondence between points of K^n and maximal ideals of the ring of exponential polynomials does not hold.
