Abstract Algebra: Theory and Applications · Problem 16.7.2

Rings — Thomas Judson

Mathematics — Abstract Algebra · rings

Problem

Let

R

be the ring of

2 \times 2

matrices of the form

\begin{pmatrix} a & b \\ 0 & 0 \end{pmatrix},

where

a, b \in \mathbb{R}

. Show that although

R

is a ring that has no identity, we can find a subring

S

R

with an identity.