
#1
Apr712, 07:25 AM

P: 19

I have in my notes that (2X,5) is an ideal of Z[X], but I can't see why this can be so.
For example 5+2X is in (2X,5) and 7+X is in Z[X] but then (5+2X)(7+X) = = 35+5X+14X+2X^2 = 2X^2+19X+35. 19 is not divisible by 2 and so this element is not in (2X,5), contradicting the "absorbance" property of ideals. 



#2
Apr712, 08:02 AM

P: 606

You seem to believe that any element in [itex](2x,5)[/itex] must have an even lineal coefficient, but this is wrong: the 5 there can multiply some xcoeff. of some pol. and added to the even coefficient in the other factor we get an odd coef. For example, the element [itex]2x\cdot 1 + 5\cdot x = 7x[/itex] belongs to the ideal... DonAntonio 


Register to reply 
Related Discussions  
Oring Query  Mechanical Engineering  3  
Ideal/Submodule Query  Linear & Abstract Algebra  1  
Real (nonideal) opamps  textbook query  Engineering, Comp Sci, & Technology Homework  1  
simple ring, maximal ideal  Calculus & Beyond Homework  2  
Ideal Gases. Query  Introductory Physics Homework  2 