Noetherian algebras and their modules

目的是研究与物理学有联系的几类重要的非交换诺瑟无穷维代数。对它们的素数谱、完全素数谱、极小谱和极大谱进行分类。生成简单模块的类。选择并研究与pi环接近的子类，并研究它们的性质。计算它们的Krull、全局和Krull维度。研究它们的左商环。开发解决上述问题的新技术。

The aim is to study some important classes of noncommutative Noetherian infinite dimensional algebras that have connection with Physics. Classify their prime, completely prime, minimal and maximal spectra. To produce classes of simple modules. Select and study subclasses that are close to PI-rings and study their properties. To calculate their Krull, global and Krull dimensions. To study their left quotients rings. To develop new techniques to tackle the above mentioned problems.