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Register a new userOn quasi – Frobenius Categories
حول الفئات شبه الفربنيوسية
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Damascus University ورقة بحثية
Publication date
1999
fields
Mathematics
and research's language is
العربية
Authors
رياض الشحيد( باحث )
Created by
Shamra Editor
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في هذا البحث يتابع الباحث أعماله السابقة إذ يقدم تمييزًا جديدًا للفئات شبه الفربنيوسية. بفرض أن C فئة صغرى سابقة الجمعية, C* الفئة الثنوية لها، فإن التتيجة الأساسية في هذا البحث هي إثبات تكافؤ الشروط التالية: ١- كل من الفئتين C* و C شبه فربنيوسية. ٢- كل مقاس منبسط على C* أو على C هو مقاس تبايني. ٣- كل مقاس تبايني على C أو على C* هو مقاس اسقاطي.
In this paper, the characterization of right and left quasi-Frobenius categories, has been given. Let C be a small preadditive category, C* the dual category of C. It has shown, that the following conditions are equivalent: (i) C is right and left quasi-Frobenius; (ii) All flat C-modules and all flat C*-modules are injective; (iii) All injective C-modules and all injective C*-modules are projective.
References used
Faith C. Algebra: Rings, modules and categories V. ١ Mir. ١٩٧٩ (in Russian).
Mitchell B. Some applications of module theory to functor categories, Bull, Amer. Math1978
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