# Certain Maximal Commutative Subrings of Full Matrix Rings

CJM Vol. 2 No. 1 (June 2010), pp. 47 – 56.

Abstract:

Denote by $M_n(R)$ the full matrix ring over a commutative ring $R$ with identity where $n > 1.$ In this paper, we show that the set $D_n(R)$ of all matrices in $M_n(R)$ of the form

\begin{bmatrix}
x_1 & 0 & \cdots & 0 & y_1 \\
0 & x_2 & \cdots & y_2 & 0 \\
\cdots & \cdots& \cdots & \cdots & \cdots \\
0 & y_2 & \cdots & x_2 & 0 \\
y_1 & 0 & \cdots & 0 & x_1 \\
\end{bmatrix}

is a maximal commutative subring of the ring $M_n(R).$

2000 Mathematics Subject Classification:

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