Show that if R is a nonzero commutative ring, then R[x] is never a field.

I'm pretty sure that it's because there cannot be an element belonging to R[x] of degree -1, but I'm not exactly sure how to express it formally.

Printable View

- Nov 30th 2009, 04:20 PMjohnt4335Commutative Rings and Fields
Show that if R is a nonzero commutative ring, then R[x] is never a field.

I'm pretty sure that it's because there cannot be an element belonging to R[x] of degree -1, but I'm not exactly sure how to express it formally. - Nov 30th 2009, 08:04 PMShanks
Hint: If R[x] is field, what is the inverse of the element x in R[x]?