Cohen-Macaulay and Gorenstein Properties of Bi-Amalgamated Algebras with Applications to Algebroid Curves
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915913209479168 |
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| author | Gürel, Efe Gündüz, Abuzer |
| author_facet | Gürel, Efe Gündüz, Abuzer |
| contents | Let $A \bowtie^{f,g} (J,J')$ be the bi--amalgamation of a commutative ring $A$ with $(B,C)$ along the ideals $(J,J')$ with respect to the ring homomorphisms $(f,g)$. In this article, we study the basic homological properties of the bi--amalgamated algebra construction. We first calculate the dimension and depth of the bi--amalgamated algebra under fairly general circumstances and derive necessary and sufficient conditions for Cohen--Macaulayness in terms of maximal and big Cohen--Macaulay modules of $A$. Furthermore, we characterize the Gorenstein property of the bi--amalgamated algebra through the canonical modules of $f(A)+J$ and $g(A)+J'$. We apply our results to the theory of curve singularities by constructing Gorenstein algebroid curves through bi--amalgamated and amalgamated algebras. We also give a brief remark concerning the universally catenary property of $A\bowtie^{f,g}(J,J')$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00266 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cohen-Macaulay and Gorenstein Properties of Bi-Amalgamated Algebras with Applications to Algebroid Curves Gürel, Efe Gündüz, Abuzer Commutative Algebra 13H10, 13B02, 13C15, 14H20 Let $A \bowtie^{f,g} (J,J')$ be the bi--amalgamation of a commutative ring $A$ with $(B,C)$ along the ideals $(J,J')$ with respect to the ring homomorphisms $(f,g)$. In this article, we study the basic homological properties of the bi--amalgamated algebra construction. We first calculate the dimension and depth of the bi--amalgamated algebra under fairly general circumstances and derive necessary and sufficient conditions for Cohen--Macaulayness in terms of maximal and big Cohen--Macaulay modules of $A$. Furthermore, we characterize the Gorenstein property of the bi--amalgamated algebra through the canonical modules of $f(A)+J$ and $g(A)+J'$. We apply our results to the theory of curve singularities by constructing Gorenstein algebroid curves through bi--amalgamated and amalgamated algebras. We also give a brief remark concerning the universally catenary property of $A\bowtie^{f,g}(J,J')$. |
| title | Cohen-Macaulay and Gorenstein Properties of Bi-Amalgamated Algebras with Applications to Algebroid Curves |
| topic | Commutative Algebra 13H10, 13B02, 13C15, 14H20 |
| url | https://arxiv.org/abs/2604.00266 |