تقرير
Some remarks on two-periodic modules over local rings
| العنوان: | Some remarks on two-periodic modules over local rings |
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| المؤلفون: | Das, Nilkantha, Dey, Sutapa |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Commutative Algebra, 13C12, 13D02, 13H10 |
| الوصف: | In this note, some properties of finitely generated two-periodic modules over commutative Noetherian local rings have been studied. We show that under certain assumptions on a pair of modules $\left(M,N \right)$ with $M$ two-periodic, the natural map $M \otimes_R N \to Hom_R(M^*,N)$ is an isomorphism. As a consequence, we have that the Auslander's depth formula holds for such a pair. Celikbas et al. recently showed the Huneke-Wiegand conjecture holds over one-dimensional domain for two-periodic modules. We generalize their result to the case of two-periodic module with rank over any one-dimensional local ring. More generally, under certain assumptions on the modules, we show that a pair of modules over an one-dimensional local ring has non-zero torsion if and only if they are Tor-independent. Comment: Some major changes are made. 12 pages. Comments are welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2307.12752 |
| رقم الأكسشن: | edsarx.2307.12752 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |