In this paper, we defined presheaf of R -algebras by means of the dual continuous maps on D and we obtained the sheaf of R -algebras which corresponds presheaf and finally we got a general result for the sheaf of R -algebras as follows, for open set $Usubset D$ , $CUwidetilde{=}Gamma(U,SD)widetilde{=} SD|DUwidetilde{=}Gamma SD|DU widetilde{=}Gamma(U,Gamma SD)$.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:In this paper, we defined presheaf of R -algebras by means of the dual continuous maps on D and we obtained the sheaf of R -algebras which corresponds presheaf and finally we got a general result for the sheaf of R -algebras as follows, for open set $Usubset D$ , $CUwidetilde{=}Gamma(U,SD)widetilde{=} SD|DUwidetilde{=}Gamma SD|DU widetilde{=}Gamma(U,Gamma SD)$.
📊
Key Findings & Data:In this paper, we defined presheaf of R -algebras by means of the dual continuous maps on D and we obtained the sheaf of R -algebras which corresponds presheaf and finally we got a general result for the sheaf of R -algebras as follows, for open set $Usubset D$ , $CUwidetilde{=}Gamma(U,SD)widetilde{=} SD|DUwidetilde{=}Gamma SD|DU widetilde{=}Gamma(U,Gamma SD)$.
💡
Conclusion & Impact:In this paper, we defined presheaf of R -algebras by means of the dual continuous maps on D and we obtained the sheaf of R -algebras which corresponds presheaf and finally we got a general result for the sheaf of R -algebras as follows, for open set $Usubset D$ , $CUwidetilde{=}Gamma(U,SD)widetilde{=} SD|DUwidetilde{=}Gamma SD|DU widetilde{=}Gamma(U,Gamma SD)$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, we defined presheaf of R -algebras by means of the dual continuous maps on D and we obtained the sheaf of R -algebras which corresponds presheaf and finally we got a general result for the sheaf of R -algebras as follows, for open set $Usubset D$ , $CUwidetilde{=}Gamma(U,SD)widetilde{=} SD|DUwidetilde{=}Gamma SD|DU widetilde{=}Gamma(U,Gamma SD)$.
Özet
Bu makalede, D dual sayıları üzerinde tanımlanan dual sürekli fonksiyonlar yardımıyla R-cebirlerinin ön-demeti tanımlanmış ve bu öndemete karşı gelen R-cebirlerinin demeti elde edilmiştir. Sonuç olarak herhangi $Usubset D$ açık altkümesi ve R-cebirlerinin demeti için, $CUwidetilde{=}Gamma(U,SD)widetilde{=} SD|DUwidetilde{=}Gamma SD|DU widetilde{=}Gamma(U,Gamma SD)$ genel sonucu elde edildi.
🔖
Cite This Article
İÇEN, İ., YILDIZ, C. (2022). A sheaf of R-algebras on the dual set of dual numbers. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 15 - Sayı: 1-2, 87–95. https://ajindex.com/articles/503253