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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.

Definition

If T and U are rings and M is a ( U , T ) -bimodule, then the triangular matrix ring R := [ T 0 M U ] consists of 2 by 2 matrices of the form [ t 0 m u ] , where t ∈ T , m ∈ M , and u ∈ U , with ordinary matrix addition and matrix multiplication as its operations.

References

Triangular matrix ring Wikipedia
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