کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4584899 | 1630513 | 2014 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Simple rings and degree maps
ترجمه فارسی عنوان
حلقه های ساده و نقشه های درجه
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
For an extension A/B of neither necessarily associative nor necessarily unital rings, we investigate the connection between simplicity of A with a property that we call A-simplicity of B. By this we mean that there is no non-trivial ideal I of B being A-invariant, that is satisfying AIâIA. We show that A-simplicity of B is a necessary condition for simplicity of A for a large class of ring extensions when B is a direct summand of A. To obtain sufficient conditions for simplicity of A, we introduce the concept of a degree map for A/B. By this we mean a map d from A to the set of non-negative integers satisfying the following two conditions: (d1) if aâA, then d(a)=0 if and only if a=0; (d2) there is a subset X of B generating B as a ring such that for each non-zero ideal I of A and each non-zero aâI there is a non-zero aâ²âI with d(aâ²)⩽d(a) and d(aâ²bâbaâ²)
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 401, 1 March 2014, Pages 201-219
Journal: Journal of Algebra - Volume 401, 1 March 2014, Pages 201-219
نویسندگان
Patrik Nystedt, Johan Ãinert,