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Register a new userDeveloping Hilbert’s Nullstellensatz into Categorical Adjunction
تَطوير نَظرية Hilbert للأصفَارِ إلى تَرافُقٍ فِئَويٍ
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تحتوي هذه الورقة على تطوير للتماثل بين فئتي المثاليات الجذرية و المجموعات الجبرية التآلفية إلى ترافق فئوي بين تشاكلين فئويين. و مدد مفهوما التشاكلين الفئويين السابقين من خلال توسيع العمل إلى فئة المثاليات في حلقة حدوديات بـ n متغيراً فوق حقل مثبت مغلق جبرياً k التـي تـشكل المثاليـات الجذرية فئة جزئية ممتلئة منها و ذلك للحصول على ترافق أعم.
This paper includes an improvement of the categorical isomorphism between the category of radical ideals and the category of affine algebraic sets into an adjunction between two functors. Afterwards, we extend the previous functors by means of expanding our work into the category of all ideals in a polynomial ring in n variables over a fixed algebraically closed field k, in which the radical ideals form a full subcategory of it, in order to produce more generalized adjunction.
References used
Adamek, J. Herrlich, H. Strecker, G. E. 2004. “Abstract and Concrete categories”, Oxford Press
Asperti, A. Longo, G. 1991. “Categories, Types and Structures”, M.I.T Press
Awdey, S., 2006. “Category Theory”, Clarendon Press – Oxford
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