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Upper triangular $2\times2$-matrices over a Baer *-ring
Let $A$ be a Baer $*$-ring. Let us denote $B$ by the space of all upper triangular matrices
$\left(\begin{array}{cc}
a_1& a_2 \\
0 & a_4
\end{array}\right)$ where $a_i$'s are in $A$. Is $B$ ...
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