Mathematical Sciences: Finite Dimensional Algebras and Artinian Rings

该项目涉及阿尔丁环的各个方面，特别是有限维代数的同调性质和模的分解性质。在第一类中，目标是更好地理解全局和有限维度。在第二种情况下，目标是获得环的表示理论，其所有左模都是有限生成分量的直接和。该研究属于环理论的一般领域。环是一种代数结构，其上定义有加法和乘法。这些物体自然产生，在数学和物理学的许多领域都很重要。

This project is concerned with various aspects of artinian rings, in particular homological properties of finite dimensional algebras and decomposition properties of modules. In the first category, the goal is to obtain a better understanding of global and finitistic dimensions. Under the second, the aim is to obtain a representation theory for rings all of whose left modules are direct sums of finitely generated components. The research is in the general area of ring theory. A ring is an algebraic structure having both an addition and a multiplication defined on it. These objects arise naturally and are important in many areas of mathematics and physics.