论文标题
Parafree增强代数和Gröbner-Shirshov基地，用于完整的增强代数
Parafree augmented algebras and Gröbner-Shirshov bases for complete augmented algebras
论文作者
论文摘要
我们开发了一种类似于旁皮群体理论的偏板增强代数的理论，并探讨了一些与偏板猜想有关的问题。我们提供了一个有限生成的无限共同体学维度的有限生成的增强代数。在此示例的激励下，我们证明了用于完整增强代数的组成钻石引理的一种版本，并为增强代数提供了足够的条件，可以对其关系的语言保持差异。
We develop a theory of parafree augmented algebras similar to the theory of parafree groups and explore some questions related to the Parafree Conjecture. We provide an example of finitely generated parafree augmented algebra of infinite cohomological dimension. Motivated by this example, we prove a version of the Composition-Diamond lemma for complete augmented algebras and provide a sufficient condition for augmented algebra to be residually nilpotent on the language of its relations.
