HOMOLOGICAL DIMENSION BASED ON A CLASS OF GORENSTEIN MODULES AND RECOLLEMENT SITUATIONS

We study the Gorenstein (ℒ,𝒜)-projective resolution dimension of modules and the left global Gorenstein (ℒ,𝒜)-projective dimension of rings in detail, where (ℒ,𝒜) represents a complete duality pair and Gorenstein (ℒ,𝒜)-projective modules were introduced by Gillespie in 2019. We give some characterizations of the (finite) Gorenstein (ℒ,𝒜)-projective resolution dimension of modules and reveal some connections between this dimension and other Gorenstein homological dimensions. We find some lower and upper bounds of the (finite) left global Gorenstein (ℒ,𝒜)-projective dimension of rings by some classical homological invariants and recollements of abelian categories.