On Homological Dimensions of S-Acts With Unique Zero
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...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2025-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/jom/5590978 |
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| Summary: | 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. |
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| ISSN: | 2314-4785 |