کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4596460 | 1336167 | 2014 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Generalized weakly symmetric rings
ترجمه فارسی عنوان
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
A ring R is defined to be GWS if abc=0 implies bacâN(R) for a,b,câR, where N(R) stands for the set of nilpotent elements of R. Since reduced rings and central symmetric rings are GWS, we study sufficient conditions for GWS rings to be reduced and central symmetric. We prove that a ring R is GWS if and only if the nÃn upper triangular matrices ring Un(R,R) is GWS for any positive integer n. It is proven that GWS rings are directly finite and left min-abel. For a GWS ring R, R is a strongly regular ring if and only if R is a von Neumann regular ring if and only if R is a left SF ring and J(R)=0; R is an exchange ring if and only if R is a clean ring. Finally, we show that GWS exchange rings have stable range 1 and a GWS semiperiodic ring R with N(R)â J(R) is commutative.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 218, Issue 9, September 2014, Pages 1594-1603
Journal: Journal of Pure and Applied Algebra - Volume 218, Issue 9, September 2014, Pages 1594-1603
نویسندگان
Junchao Wei,