I would like to find a ring that is left semisimple but not right semisimple. I know that it should be non unitary, and non semiprime, but I can't find an example of a non semiprime ring, I just find examples of rings that are semisimple and semiprimes when I look for it.
I just need an example of a non semiprime ring, but the ring that is semisimple just one side would be welcome.
Thanks in advance.