We know that a simple ring has characteristic either $ 0 $ or a prime $ p $. I am thinking about giving a concrete example of a simple ring WITH zero divisors.
I have found a reference talking about simple rings without zero-divisors:
2026-03-28 02:59:27.1774666767
Ask for example: A simple ring with zero divisors
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A matrix ring $M_n(R)$ when $R$ is a simple ring, is also simple. For instance one can take $R$ to be one's favourite field. Matrix rings generally have zero divisors.