Difficult)
I'm struggling to see the value and usefulness in not having a zero divisor, or similarly in having an integral domain. I need to review and re-apply the understanding of the integral domain so that I understand it's application better.
After reviewing a lot of different websites, I'm still stumped...I was getting caugth up on the definition of the O and 1...no not binary, but the additive identity O and the multiplicative identity 1
The integral domain is dependant on the existance of both and that they are not the same. There are some rings for which the additive and the multiplicative are the same. The integral domain is a distinction that forces these to be diferent, or that 1 does not equal 0.
Inspiring/Relational idea)
It looks like a unit is a field that doesn't commute. but that there is also a unique solution to au=1 instead of simply having a solution for any a in the ring. The unique solution is a very powerful tool in defining the tool if subtraction, Very useful way to manipulate rings that are not commutitive!!!
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