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Ring of matrices over a field is isomorphic to the field

Source: RomNO 2003, grade xii. p. 1

August 27, 2019
linear algebraabstract algebraRing TheoryIsomorphisms

Problem Statement

a) 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) Prove that (Mn(R),+,⋅)≇(Mn(C),+,⋅), \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≥2. n\ge 2.
Marian Andronache, Ion Sava
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