Universal Algebras and Residual Finiteness

该项目将集中在通用代数上，并旨在对某些代数品种的剩余有限进行分类，以及观察直接和次直接乘积的剩余有限。特别地，一个目的是试图找到代数类型的充分必要条件，以得出当且仅当其分量是剩余有限的直积是剩余有限的结论。我们也将探讨代数结构的子代数可分性和有限可分性的相关概念。至少有100小时的SMSTC模块工作经验。

The project will be focussed around universal algebra, and aim at classifying when certain varieties of algebra are residually finite, as well as looking at residual finiteness of direct and subdirect products. I particular, one aim would be to try and find necessary and sufficient conditions on the type of an algebra to conclude that a direct product is residually finite if and only if its components are residually finite. There will also be investigation into the related notions of subalgebra separability and finite divisibility of algebraic structures.At least 100 hours of work in SMSTC modules.