论文标题
小取消戒指
Small cancelation rings
论文作者
论文摘要
小型取消组的理论是众所周知的。在本文中，我们介绍了类似小组的小取消环的概念。这是论文的主要结果。我们通过发电机和定义关系公理地定义了这个环。关系必须满足三种类型的公理。其中的主要一个称为小取消公理。我们表明获得的环是非平凡的。此外，我们表明该戒指具有与关系一致的全球过滤，找到戒指作为向量空间的基础并建立相应的结构定理。事实证明，定义的戒指具有某种基础和贪婪的算法。最后，该环可以用作迈向迭代的小型取消理论的第一步，该理论希望在构建具有异国特性的环的示例中起着与小型取消组在群体理论中所做的相似作用。这是Paper Arxiv的简短版本：2010.02836
The theory of small cancellation groups is well known. In this paper we introduce the notion of Group-like Small Cancellation Ring. This is the main result of the paper. We define this ring axiomatically, by generators and defining relations. The relations must satisfy three types of axioms. The major one among them is called the Small Cancellation Axiom. We show that the obtained ring is non-trivial. Moreover, we show that this ring enjoys a global filtration that agrees with relations, find a basis of the ring as a vector space and establish the corresponding structure theorems. It turns out that the defined ring possesses a kind of Gröbner basis and a greedy algorithm. Finally, this ring can be used as a first step towards the iterated small cancellation theory which hopefully plays a similar role in constructing examples of rings with exotic properties as small cancellation groups do in group theory. This is a short version of paper arXiv:2010.02836
