On Homological Dimensions of S-Acts With Unique Zero - Elahe Nafarieh Talkhooncheh; Hamid Rasouli; Maryam Salimi; Elham Tavasoli; Abolfazl Tehranian (Journal of Mathematics)
In this paper, we introduce homological dimensions of S-acts for a commutative monoid S with a zero element and analyze their properties. We define projective (flat) dimension by means of double-arrow complexes and construct an injective resolution of an S-act. It is shown that the flat dimension of an S-act is a refinement of a projective dimension. For an S-act X and a multiplicatively closed subset T of S, we prove that the projective (flat) dimension of the localization T−1X, as a T−1S-act, is less than or equal to the projective (flat) dimension of X.