论文标题
圆环的类似小组小型取消理论
Group-like small cancellation theory for rings
论文作者
论文摘要
在本文中，我们为具有可逆元素的基础的联想代数开发了一个小的取消理论。也就是说，我们研究自由组的组代数的商，并为相应的定义关系引入三个公理。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。我们还为我们的戒指提供了一个格格纳基础概念的修订，并为理想的会员问题建立了一种贪婪的算法。
In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding defining relations. 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. We also provide a revision of a concept of Gröbner basis for our rings and establish a greedy algorithm for the Ideal Membership Problem.
