Let be a polynomial with complex coefficients and with the degree (http://planetmath.org/Polynomial) . If can not be written as product of two polynomials with positive degrees and with coefficients in the field , then the polynomial is said to be . Otherwise, is reducible.
Examples. All linear polynomials are . The polynomials , and are (although they split in linear factors in the fields , and , respectively). The polynomials and are not .
The above definition of polynomial is special case of the more general setting where is a non-constant polynomial in the polynomial ring of a field ; if is not expressible as product of two polynomials with positive degrees in the ring , then is (in ).
|Date of creation||2013-03-22 14:24:22|
|Last modified on||2013-03-22 14:24:22|
|Last modified by||pahio (2872)|