polynomial ring which is PID
with and certain polynomials in . From these equations one infers that is a polynomial and is a first degree polynomial (). Thus we obtain the equation
which shows that is the unity 1 of . Thus is a unit of , whence
So we can write
where . This equation cannot be possible without that times the constant term of is the unity. Accordingly, has a multiplicative inverse in . Because was arbitrary non-zero elenent of the integral domain , is a field.
- 1 David M. Burton: A first course in rings and ideals. Addison-Wesley Publishing Company. Reading, Menlo Park, London, Don Mills (1970).
|Title||polynomial ring which is PID|
|Date of creation||2013-03-22 17:53:04|
|Last modified on||2013-03-22 17:53:04|
|Last modified by||pahio (2872)|