Mirai Ikebuchi. Homological Methods in Rewriting (invited talk)
Channel: Computational Logic and Applications
Date: 2020-10-12

15th Workshop
Computational Logic and Applications (https://cla.tcs.uj.edu.pl/)
12-13 October 2020

Speaker: Mirai Ikebuchi
Title: Homological Methods in Rewriting (invited talk)
Abstract:
It is well-known that some equational theories such as groups or boolean algebras can be defined by fewer equational axioms than the original axioms. However, it is not easy to determine if a given set of axioms is the smallest or not. In this talk, we will see a way to find a lower bound of the number of axioms. The inequality that gives the lower bound is obtained by analyzing the algebraic structure, called the homology group, associated with the given equational theory. I will explain how equational theories and rewriting systems relate to abstract algebra, what homology groups in general settings are like, and what the homology groups of equational theories give us.