Triangular matrix ring

In algebra, a triangular matrix 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 (T 0
M U) consists of 2 by 2 matrices (t 0
m u) with t ∈ T, m ∈ M, u ∈ U, with ordinary matrix multiplication and division.

References

• Auslander, Maurice; Reiten, Idun; Smalø, Sverre O. (1997) [1995], Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics 36, Cambridge University Press, ISBN 978-0-521-59923-8, MR 1314422