On Homological Dimensions of S-Acts With Unique Zero

Elahe Nafarieh Talkhooncheh, Hamid Rasouli, Maryam Salimi, Elham Tavasoli and Abolfazl Tehranian

Journal of Mathematics, 2025, vol. 2025, 1-7

Abstract: 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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5590978

DOI: 10.1155/jom/5590978

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