Proper Zero Divisor/Examples/Ring of Order 2 Complex Matrices
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Example of Proper Zero Divisor
Consider the ring of square matrices $\struct {\map {\MM_\C} 2, +, \times}$ of order $2$ over the complex numbers $\C$.
We have:
- $\begin {pmatrix} 1 & i \\ i & -1 \end {pmatrix} \begin {pmatrix} 1 & i \\ i & -1 \end {pmatrix} = \begin {pmatrix} 0 & 0 \\ 0 & 0 \end {pmatrix}$
demonstrating that $\begin {pmatrix} 1 & i \\ i & -1 \end {pmatrix}$ is a proper zero divisor of $\struct {\map {\MM_\C} 2, +, \times}$.
Sources
- 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 2$. Elementary Properties