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Math Help - Commutative Rings and Fields

  1. #1
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    Commutative 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.
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  2. #2
    Senior Member Shanks's Avatar
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    Hint: If R[x] is field, what is the inverse of the element x in R[x]?
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