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Parafree augmented algebras and Gröbner-Shirshov bases for complete augmented algebras
Journal of Pure and Applied Algebra ( IF 0.8 ) Pub Date : 2021-03-17 , DOI: 10.1016/j.jpaa.2021.106725
Sergei O. Ivanov , Viktor Lopatkin

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 a 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 give a sufficient condition for an augmented algebra to be residually nilpotent in terms of its relations.



中文翻译:

完全自由的代数的Parafree扩充代数和Gröbner-Shirshov基

我们开发了一种类似于无源自由群理论的无源自由代数理论,并探讨了与无源猜想有关的一些问题。我们提供了一个无限生成的,具有无限同调维数的无位自由无穷扩充代数的例子。受此示例的启发,我们证明了完全增量代数的Composition-Diamond引理的一种形式,并给出了一个充分的条件,使增量代数在其关系方面保持零幂。

更新日期:2021-03-24
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