Year: 2025
Type: article
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 −1 X , as a T −1 S ‐act, is less than or equal to the projective (flat) dimension of X .
Source: Journal of Mathematics
DOI: 10.1155/jom/5590978
Authors: Elahe Nafarieh Talkhooncheh, Hamid Rasouli, Maryam Salimi, Elham Tavasoli, Abolfazl Tehranian
Institution: Islamic Azad University, Tehran
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,160
OpenAlex ID: W4412464309