polynomial ring over integral domain
Proof. Let and be two non-zero polynomials in and let and be their leading coefficients, respectively. Thus , , and because has no zero divisors, . But the product is the leading coefficient of and so cannot be the zero polynomial. Consequently, has no zero divisors, Q.E.D.
Remark. The theorem may by induction be generalized for the polynomial ring .
|Title||polynomial ring over integral domain|
|Date of creation||2013-03-22 15:10:06|
|Last modified on||2013-03-22 15:10:06|
|Last modified by||pahio (2872)|