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Date: 13-2-2019
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Date: 4-3-2019
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A polynomial admitting a multiplicative inverse. In the polynomial ring , where is an integral domain, the invertible polynomials are precisely the constant polynomials such that is an invertible element of . In particular, if is a field, the invertible polynomials are all constant polynomials except the zero polynomial.
If is not an integral domain, there may be in invertible polynomials that are not constant. In , for instance, we have:
which shows that the polynomial is invertible, and inverse to itself.
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