التفاصيل البيبلوغرافية
| العنوان: |
On equivalence of some subcategories of modules in Morita contexts |
| المؤلفون: |
Kashu, A. I. |
| المصدر: |
Algebra and Discrete Mathematics; Vol 2, No 3 (2003) ; 2415-721X ; 1726-3255 |
| بيانات النشر: |
Lugansk National Taras Shevchenko University |
| سنة النشر: |
2018 |
| مصطلحات موضوعية: |
torsion (torsion theory), Morita context, torsion free module, accessible module, equivalence, 16S90, 16D90 |
| الوصف: |
A Morita context \((R,\,_{R}\!V_{S},\,_{S}\!W_{R},S)\) defines the isomorphism \({\cal L}_{0}(R) \cong {\cal L}_{0}(S)\) of lattices of torsions \(r\geq r_{\scriptscriptstyle I}\) of \(R\)-\(Mod\) and torsions \(s\geq r_{\scriptscriptstyle J}\) of \(S\)-\(Mod\), where \(I\) and \(J\) are the trace ideals of the given context. For every pair \((r,s)\) of corresponding torsions the modifications of functors \(T^{W}=W\otimes _{R}\)- and \(T^{V}=V\otimes _{S}\)- are considered:\[R\textrm{-}Mod\supseteq \mathcal{P}(r)\begin{array}{c}\begin{array}{c}\underrightarrow{\quad\bar{T}^W=(1/s)\cdot T^W\quad}\\\overleftarrow{\quad\bar{T}^V=(1/r)\cdot T^{V}\quad}\end{array}\end{array}\mathcal{P}(s)\subseteq S\textrm{-}Mod,\]where \({\cal P}(r)\) and \({\cal P}(s)\) are the classes of torsion free modules. It is proved that these functors define the equivalence \begin{equation*} {\cal P}(r)\cap {\cal J}_{I}\approx {\cal P}(s)\cap {\cal J}_{J}, \end{equation*} where \({\cal P}(r)=\{_{R}M\ |\ r(M)=0\}\) and \({\cal J}_{I}=\{_{R}M\ |\ IM=M\}.\) |
| نوع الوثيقة: |
article in journal/newspaper |
| وصف الملف: |
application/pdf |
| اللغة: |
English |
| Relation: |
http://admjournal.luguniv.edu.ua/index.php/adm/article/view/963/492; http://admjournal.luguniv.edu.ua/index.php/adm/article/view/963 |
| الاتاحة: |
http://admjournal.luguniv.edu.ua/index.php/adm/article/view/963 |
| Rights: |
Copyright (c) 2018 Algebra and Discrete Mathematics |
| رقم الانضمام: |
edsbas.795826F0 |
| قاعدة البيانات: |
BASE |