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On Homological Dimensions of S-Acts With Unique Zero

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  • Elahe Nafarieh Talkhooncheh
  • Hamid Rasouli
  • Maryam Salimi
  • Elham Tavasoli
  • Abolfazl Tehranian

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.

Suggested Citation

  • Elahe Nafarieh Talkhooncheh & Hamid Rasouli & Maryam Salimi & Elham Tavasoli & Abolfazl Tehranian, 2025. "On Homological Dimensions of S-Acts With Unique Zero," Journal of Mathematics, Hindawi, vol. 2025, pages 1-7, July.
    • Handle: RePEc:hin:jjmath:5590978
    DOI: 10.1155/jom/5590978
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