Abstract:

By means of homological algebra, some equivalent characterizations were given when R was left GP-injective ring, left GPP-ring or left GPF-ring. Having introduced the notions of GP-injective dimensions and GP-flat dimensions, we proved that left GP-injective global dimension is equal to right GP-weak dimension of R under the condition that R is left P-coherent. Furthermore, some new characterizations of GP-injective dimensions and GP-flat dimensions were also given.

Key words: GP-flat module, GP-injective module, GP-flat dimension； GP-injective dimension