Triangular matrix ring
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In algebra, a triangular matrix ring, also called a triangular ring, is a ring constructed from two rings and a bimodule.
In algebra, a triangular matrix ring, also called a triangular ring, is a ring constructed from two rings and a bimodule. ==Definition== If T and U are rings and M is a \left(U,T\right) -bimodule, then the triangular matrix ring R:=\left[\begin{array}{cc}T&0\\M&U\\\end{array}\right] consists of 2-by-2 matrices of the form \left[\begin{array}{cc}t&0\\m&u\\\end{array}\right] , where t\in T,m\in M, and u\in U, with ordinary matrix addition and matrix multiplication as its operations. ==References==
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