مشاركة
التوسيعات الراشدة والاغمارية == RATIONAL EXTENSIONS AND INJECTIVITY
اسم المؤلف:
مهدي صالح نايف
اسم المشرف:
مهدي صادق عباس
الموضوع العام:
علوم الرياضيات
السنة:
2015
الموضوع الدقيق:
الرياضيات
الدرجة:
دكتوراه
الجامعة:
الجامعة المستنصرية - كلية التربية للبنات - قسم الرياضيات
اللغة:
الانكليزية
مكان الجامعة:
بغداد
الصفحات الاولى:
27T993 - p.pdf
المستخلص:
In this work, many of generalizations of injectivity are introduced and studied by using rational submodules and rationally closed submodules. The nation of (pseudo - ) injective modules is generalized to that of rationally (pseudo - )injective modules. On the other hand, the notions of (quasi - )injective modules and pseudo - injective modules are also generalized to that of RC - (quasi - )injective and pseudo - RC - injective modules respectively.Numerous properties and characterizations of these generalizations are given. Moreover, the relation between these notions is studied. Several known modules are characterization in terms of some of these concepts such as semisimple, rationally extending. Also, sufficient conditions for a direct sum of two rationally extending modules to be rationally extending are considered. The connections between some of these concepts and some other modules such as Hopfain, Co - Hopfain, divisible modules are discussed. Also, semisimple artinian rings, SI - rings have been characterized in terms of some of these concepts.
