A topological structure on certain initial algebras
A topological structure on certain initial algebras
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某些初始代数的拓扑结构
DOI：
10.1016/j.topol.2014.11.008
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发表时间：
2015
影响因子：
0.6
通讯作者：
Jeremy Usatine
中科院分区：
文献类型：
--
作者：
S. Anderson;Andrew L. Smith;Peter Stewart;Mohammed Tesemma;Jeremy Usatine
在群的相容全序集上有一个著名的自然拓扑，Clay [2]，Dabkowska et al. [4]和Sikora [12]的最近结果刻画了某些群的这个拓扑。我们考虑多项式环和Laurent多项式环中不同单项代数集合上的一个相似拓扑。我们研究了后者的拓扑结构的单项代数，来自环的乘法不变量，并表明，他们要么是有限的离散空间或同胚的康托集。
There is a well-known natural topology on the set of compatible total orders on a group, and recent results of Clay [2], Dabkowska et al. [4], and Sikora [12] have characterized this topology for certain groups. We consider a similar topology on the set of distinct monomial algebras in polynomial and Laurent polynomial rings. We study the latter topological structure for monomial algebras that come from rings of multiplicative invariants and show that they are either finite discrete spaces or homeomorphic to the Cantor set.