Triangular matrix ring

In algebra, a triangular matrix ring, also called a triangular ring, is a ring constructed from two rings and a bimodule.

Definition

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If   and   are rings and   is a  -bimodule, then the triangular matrix ring   consists of 2-by-2 matrices of the form  , where   and   with ordinary matrix addition and matrix multiplication as its operations.

References

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