On ${\tau }_q$-weak global dimensions of commuative rings

In this paper, the ${\tau }_q$-weak global dimension ${\tau }_q$-\cwd$(R)$ of a commutative ring $R$ is introduced. Rings with ${\tau }_q$-weak global dimension equal to $0$ are studied in terms of homologies, direct products, polynomial extensions and amalgamations. Besides, we investigate the ${\tau }_q$-weak global dimensions of polynomial rings.