The discussion revolves around the relationship between ideals in the polynomial ring F[x], specifically examining the condition I ⊆ J and its equivalence to the divisibility of polynomials, g(x) dividing f(x).
Participants are actively engaging with the definitions and implications of ideals, with some confirming understanding and others seeking clarification on specific terms and concepts. There is a productive exchange regarding the relationship between the ideals and the polynomials involved.
Participants are discussing the definitions and properties of ideals in the context of polynomial rings, with a focus on the implications of these definitions for the relationship between the polynomials f(x) and g(x).
Correct.phyguy321 said:If I is a subset of J then does that mean that f is in J
Sort of. I would just use the fact that J is generated by g(x).also and by definition of an ideal g*some b in J must equal something in J so g|f? because g|f means that f=bg for some b in J