Invariants of linkage of modules
| العنوان: | Invariants of linkage of modules |
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| المؤلفون: | Tony J. Puthenpurakal |
| المصدر: | MATHEMATICA SCANDINAVICA. 127:223-242 |
| بيانات النشر: | Det Kgl. Bibliotek/Royal Danish Library, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Linkage (software), Mathematics::Commutative Algebra, General Mathematics, Mathematics::Rings and Algebras, Local ring, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Primary 13C40, Secondary 13D07, Negative - answer, Combinatorics, Mathematics::K-Theory and Homology, FOS: Mathematics, Ideal (ring theory), Finitely-generated abelian group, Mathematics::Representation Theory, Mathematics |
| الوصف: | Let $(A,\mathfrak{m})$ be a Gorenstein local ring and let $M$, $N$ be two Cohen-Macaulay $A$-modules with $M$ linked to $N$ via a Gorenstein ideal $\mathfrak{q}$. Let $L$ be another finitely generated $A$-module. We show that $\mathrm{Ext}^i_A(L,M) = 0 $ for all $i \gg 0$ if and only if $\mathrm{Tor}^A_i(L,N) = 0$ for all $i \gg 0$. If $D$ is a Cohen-Macaulay module then we show that $\mathrm{Ext}^i_A(M, D) = 0 $ for all $i \gg 0$ if and only if $\mathrm{Ext}^i_A(D^\dagger , N) = 0$ for all $i \gg 0$, where $D^\dagger = \mathrm{Ext}^r_A(D,A)$ and $r = \mathrm{codim}(D)$. As a consequence we get that $\mathrm{Ext}^i_A(M, M) = 0 $ for all $i \gg 0$ if and only if $\mathrm{Ext}^i_A(N, N) = 0$ for all $i \gg 0$. We also show that $\mathrm{End}_A(M)/\mathrm{rad}\,\mathrm{End}_A(M) \cong (\mathrm{End}_A(N)/\mathrm{rad}\,\mathrm{End}_A(N))^{\mathrm{op}}$. We also give a negative answer to a question of Martsinkovsky and Strooker. |
| تدمد: | 1903-1807 0025-5521 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f4b83a43420cc20729f1fce4d12a2027 https://doi.org/10.7146/math.scand.a-125992 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....f4b83a43420cc20729f1fce4d12a2027 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 19031807 00255521 |
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