کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4599889 | 1336826 | 2013 | 5 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
When is every linear transformation a sum of two commuting invertible ones?
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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چکیده انگلیسی
A well-known result of Wolfson [7] and Zelinsky [8] says that every linear transformation of a vector space V over a division ring D is a sum of two invertible linear transformations except when dim(V)=1 and D=F2. Indeed, many of these linear transformations satisfy a stronger property that they are sums of two commuting invertible linear transformations. The goal of this note is to prove that every linear transformation of a vector space V over a division ring D is a sum of two commuting invertible ones if and only if |D|⩾3 and dim(V)<â. As a consequence, a sufficient and necessary condition is obtained for a semisimple module to have the property that every endomorphism is a sum of two commuting automorphisms.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 439, Issue 11, 1 December 2013, Pages 3615-3619
Journal: Linear Algebra and its Applications - Volume 439, Issue 11, 1 December 2013, Pages 3615-3619
نویسندگان
Gaohua Tang, Yiqiang Zhou,