On bi-amalgamated constructions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913290603462656 |
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| author | Campanini, Federico Finocchiaro, Carmelo Antonio |
| author_facet | Campanini, Federico Finocchiaro, Carmelo Antonio |
| contents | Let $f:A\longrightarrow B, g:A\longrightarrow C$ be ring homomorphisms and let $\mathfrak{b}$ (resp., $\mathfrak{c}$) be an ideal of $B$ (resp., $C$) satisfying $f^{-1}(\mathfrak{b})=g^{-1}(\mathfrak{c})$. Recently Kabbaj, Louartiti and Tamekkante defined and studied the following subring $$A\bowtie^{f,g}(\mathfrak{b},\mathfrak{c}) :=\{(f(a)+b, g(a)+c)\mid a\in A, b\in\mathfrak{b}, c\in \mathfrak{c} \}$$ of $B\times C$, called the bi-amalgamation of $A$ with $(B,C)$ along $(\mathfrak{b}, \mathfrak{c})$, with respect to $(f,g)$. This ring construction is a natural generalization of the amalgamated algebras, introduced and studied by D'Anna, Finocchiaro and Fontana. The aim of this paper is to continue the investigation started by Kabbaj, Louartiti and Tamekkante, by providing a deeper insigt on the ideal-theoretic structure of bi-amalgamations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_20224 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On bi-amalgamated constructions Campanini, Federico Finocchiaro, Carmelo Antonio Commutative Algebra Let $f:A\longrightarrow B, g:A\longrightarrow C$ be ring homomorphisms and let $\mathfrak{b}$ (resp., $\mathfrak{c}$) be an ideal of $B$ (resp., $C$) satisfying $f^{-1}(\mathfrak{b})=g^{-1}(\mathfrak{c})$. Recently Kabbaj, Louartiti and Tamekkante defined and studied the following subring $$A\bowtie^{f,g}(\mathfrak{b},\mathfrak{c}) :=\{(f(a)+b, g(a)+c)\mid a\in A, b\in\mathfrak{b}, c\in \mathfrak{c} \}$$ of $B\times C$, called the bi-amalgamation of $A$ with $(B,C)$ along $(\mathfrak{b}, \mathfrak{c})$, with respect to $(f,g)$. This ring construction is a natural generalization of the amalgamated algebras, introduced and studied by D'Anna, Finocchiaro and Fontana. The aim of this paper is to continue the investigation started by Kabbaj, Louartiti and Tamekkante, by providing a deeper insigt on the ideal-theoretic structure of bi-amalgamations. |
| title | On bi-amalgamated constructions |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2403.20224 |