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Found problems: 1

2003 Romania National Olympiad, 1
Tags: linear algebra , abstract algebra , Ring Theory , Isomorphisms
[b]a)[/b] Determine the center of the ring of square matrices of a certain dimensions with elements in a given field, and prove that it is isomorphic with the given field. [b]b)[/b] Prove that $$ \left(\mathcal{M}_n\left( \mathbb{R} \right) ,+, \cdot\right)\not\cong \left(\mathcal{M}_n\left( \mathbb{C} \right) ,+,\cdot\right) , $$ for any natural number $ n\ge 2. $ [i]Marian Andronache, Ion Sava[/i]