کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602403 1631170 2008 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Commuting graphs of full matrix rings over finite fields
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Commuting graphs of full matrix rings over finite fields
چکیده انگلیسی

Let R be a non-commutative ring and Z(R) be its center. The commuting graph of R is defined to be the graph Γ(R) whose vertex set is R⧹Z(R) and two distinct vertices are joint by an edge whenever they commute. Let F be a finite field, n⩾2 an arbitrary integer and R be a ring with identity such that Γ(R)≅Γ(Mn(F)), where Mn(F) is the ring of n×n matrices over F. Here we prove that |R|=|Mn(F)|. We also show that if |F| is prime and n=2, then R≅M2(F).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 428, Issues 11–12, 1 June 2008, Pages 2947-2954