Noetherian algebras and their modules

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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.