Study of artinian rings with Morita duality

点击翻译按钮获取中文摘要

Azumaya's conjecture "every exact ring has a self-duality" is an important problem in the study of Morita duality of rings. For finite triangular extensions , which are closely related to exact rings, it is well-known that these ring extensions inherit Morita duality from base rings. In the study, we show that finite triangular extensions are Morita dual to finite triangular extensions. We also prove self-duality of certain finite triangular extensions of division rings. These results provide supporting evidence for Azumaya's conjecture.