divisibility by product
Proof. The divisibility assumptions that where and are some elements of . Because is a Bézout ring, there exist such elements and of that . This implies the equation which shows that is divisible by , i.e. , . Consequently, , or Q.E.D.
Note 1. The theorem may by induction be generalized for several factors (http://planetmath.org/Divisibility) of .
|Title||divisibility by product|
|Date of creation||2013-03-22 14:50:37|
|Last modified on||2013-03-22 14:50:37|
|Last modified by||pahio (2872)|