Mathematical Sciences: Universal Algebra and Lattice Theory

这个项目是关于普遍代数和格理论的基本问题的研究。具体的研究领域将是研究有限表示格中某些算法的复杂性；模同余变量；关于直接分解的ores定理和Jonsson定理的一般推广的确定；处理有限表示格的计算机代数系统的发展以及素域上的投影平面。格是离散的数学对象，其结构在一定程度上反映了集合论或逻辑的结构。这种非常弱的结构意味着可以在许多数学环境中找到格。这也意味着问题很容易表述，很难解决，并且具有非常普遍的性质。

This project is concerned with the study of basic problems in universal algebra and lattice theory. The specific areas of investigation will be the study of the complexity of certain algorithms in finitely presented lattices; modular congruence varieties; the determination of a common generalization to Ore's and Jonsson's theorems on direct decompositions; development of a computer algebra system dealing with finitely presented lattices; and projective planes over prime fields. Lattices are discrete mathematical objects with a structure reflecting to some extent the structure of set theory or logic. This very weak structure means that lattices can be found in many mathematical environments. It also means that problems are easy to state, difficult to solve and of a very general nature.