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I was helping someone with a problem today, and it was about showing that ##\mathbb{Z_2}## was a field. It's been a while since I've done abstract algebra, but to my knowledge, this means that there has to exist a multiplication inverse for 0? But I don't see how it would be allowed in this set.
##0*a=1 \rightarrow 0=a^{-1}## but ##0*0=0##. Is there something I'm overlooking? Potentially my math is off too, any insights would be helpful.
##0*a=1 \rightarrow 0=a^{-1}## but ##0*0=0##. Is there something I'm overlooking? Potentially my math is off too, any insights would be helpful.