论文标题
带有真实指数的多项式环上的必要分级代数
Essential graded algebra over polynomial rings with real exponents
论文作者
论文摘要
单一理想和多层模块的几何和代数理论是在实际的多项式环上启动的，更一般而言，是真实多面体锥的单型代数。主要结果包括对Nakayama的引理的概括；完整的理论最少和致密的原发性，次要和不可约合的分解，包括相关和附着的面孔； Socles and Tops；减少船体，不适的盖子和边缘演示的最小和密度； Matlis二元性；和楼梯的几何分析。半分布或分段线性（PL）的模块具有功能构造以及最小的原发性和次要分解的相关属性。当所讨论的模块是组本身的亚序列时，例如单一理想和商人模仿它们时，最小的原发性和次要分解是规范的，而不可减少的分解也是如此，直到新的实现密度概念。
The geometric and algebraic theory of monomial ideals and multigraded modules is initiated over real-exponent polynomial rings and, more generally, monoid algebras for real polyhedral cones. The main results include the generalization of Nakayama's lemma; complete theories of minimal and dense primary, secondary, and irreducible decomposition, including associated and attached faces; socles and tops; minimality and density for downset hulls, upset covers, and fringe presentations; Matlis duality; and geometric analysis of staircases. Modules that are semialgebraic or piecewise-linear (PL) have the relevant property preserved by functorial constructions as well as by minimal primary and secondary decompositions. And when the modules in question are subquotients of the group itself, such as monomial ideals and quotients modulo them, minimal primary and secondary decompositions are canonical, as are irreducible decompositions up to the new real-exponent notion of density.
