a) A ring with 1 is called simple if and are the only two-sided ideals of .
If is a Artinian ring then left simple ring is right simple. By the Artin-Wedderburn theorem, a ring is simple and (left or right) Artinian if and only if ( be the ring of matrices with entries from ) for some division ring and some integer .
every ring that the statement is incorrect because
subject to the problem every left simple ring
where ideals of , is not and
in the general case.
b) Every simple ring is left simple is correct. A ring with 1 is called simple if (0) and are the only two-sided ideals of .
Subject to the problem every simple ring
where ideals of , is not and . Whereas
is left simple ring
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