Infinite examples of cancellative monoids that do not always have least common multinle.
Infinite examples of cancellative monoids that do not always have least common multinle.
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取消幺半群的无限例子并不总是具有最小公倍数。
DOI：
10.1007/s10013-014-0062-6
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发表时间：
2014
影响因子：
0.8
通讯作者：
Tadashi Ishibe
中科院分区：
文献类型：
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作者：
Kaori Kuroda;Hiroki Hashiguchi;Tohru Ikeguchi;大薮 海;大薮 海;大薮 海;大薮 海;丁 智恵;丁 智恵;Jihye Chung;丁 智恵;丁 智恵;萩野 靖乃;Tadashi Ishibe
我们将研究不包含两条平行线的复化真实的仿射线排列的补的基本群的表示。利用Yoshinaga的极小表示，我们可以给出基本群的正齐次表示。我们认为相关的幺半群定义的介绍。事实证明，在某些情况下，左（resp。右）最小公倍数并不总是存在。因此，幺半群既不是GarsidenorArtin。然而，我们将表明，他们携带某些特定的元素类似于基本元素的Artin幺半群，并通过改进的经典方法在组合群论，他们是一个cancellative幺半群。因此，我们将表明，字的问题可以解决，他们的中心是确定的。
We will study the presentations of fundamental groups of the complement of complexified real affine line arrangements that do not contain two parallel lines. By Yoshinaga’s minimal presentation, we can give positive homogeneous presentations of the fundamental groups. We consider the associated monoids defined by the presentations. It turns out that, in some cases, left (resp. right)least common multipledoes not always exist. Hence, the monoids are neitherGarsidenorArtin. Nevertheless, we will show that they carry certain particular elements similar to thefundamental elementsin Artin monoids and that, by improving the classical method in combinatorial group theory, they arecancellative monoids. As a result, we will show that the word problem can be solved and the center of them is determined.