Non commutative ring and polynomial faggotry

Howdy, chaps ?

Say, has any one really been far even as to do look more like ?

Consider a polynom with coefficients over a non-commutative ring. How do you define roots of such a polynom ? Basicly, how do you define the induced factorisation of such a polynom ? What can you tell about the aforementionned root (numbers, relations, sauce) ?

And the least important part to us mathematicians : is this useful for anything ?

>>4
I really only picked it up because of the title.  Knowing a little about it might have helped.
I didn't realize, for example, that it's really about math and not a little book of anecdotes about math teachers.