Give an example of a noncommutative ring such that and the opposite ring are not isomorphic.
I am thinking about the ring , where is any ring. But I have trouble showing that there is no isomorphism between and . Some help please.
Give an example of a noncommutative ring such that and the opposite ring are not isomorphic.
I am thinking about the ring , where is any ring. But I have trouble showing that there is no isomorphism between and . Some help please.
before giving you an example, i should explain the case define by see that is a ring isomorphism. so, if is commutative, then
an example of a ring for which is the Klein four ring, i.e. here is why:
is the only non-zero nilpotent element of and thus if is an isomorphism, then thus and so we'll get the following contradiction: