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?
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
When is every linear transformation a sum of two commuting invertible ones?
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)<∞. 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
نویسندگان
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