格多面体的无限闵可夫斯基和
Infinite Minkowski sums of lattice polyhedra
AI总结：
本文研究一类可唯一表示为整闭单项式理想无限乘积的单项式子模，其牛顿多面体对应简单格多面体的无限闵可夫斯基和，从而构造出拓扑唯一分解整环的新例子。
摘要：
Artin整闭单项式理想由其牛顿多面体刻画，这些牛顿多面体是位于正象限内、并以正象限为衰退锥的格多面体。此类理想的乘法对应于其牛顿多面体的闵可夫斯基加法。在二维情形下，Crispin-Quinonez证明了Artin整闭单项式理想在乘法下构成的同构幺半群，或上述格多面体类在闵可夫斯基加法下构成的同构幺半群，是自由阿贝尔群。Bayer和Stillman研究了洛朗多项式环中所谓的“单项式子模”。受此启发，我们考虑一族这样的单项式子模，它们可以（唯一地）表示为同构于整闭单项式理想的单项式子模的无限乘积。从几何上看，它们的牛顿多面体表示为简单格多面体的无限闵可夫斯基和。这给出了拓扑唯一分解整环（topological ufd）的另一个例子，即一个拓扑阿贝尔幺半群，其中每个元素都可以唯一地写成不可约元的收敛（可能无限）乘积。
英文摘要：
Artinian integrally closed monomial ideals are characterized by their Newton polyhedra, which are lattice polyhedra inside the positive orthant having the positive orthant as their recession cone. Multiplication of such ideals correspond to Minkowski addition of their Newton polyhedra. In two dimensions, the isomorphic monoids of artinian, integrally closed monomial ideals under multiplication, or the class of lattice polyhedra described above, under Minkowski addition, are free abelian, as proved by Crispin-Quinonez. Bayer and Stillman considered so-called /monomial submodules/ of the Laurent polynomial ring. Inspired by this, we consider a family of such monomial submodules that can be (uniquely) expressed as an infinite product of monomial submodules isomorphic to integrally closed monomial ideals. Geometrically, their Newton polyhedras are expressed as an infinite Minkowski sum of *simple* lattice polyhedra. This gives another example of a *topological ufd* i.e. a topological abelian monoid in which every element can be uniquely written as a convergent (possibly infinite) product of irreducibles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
