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Metric_Space said:
polynomials of what form?
What does the following subring of the complex numbers look like
- Thread starter Metric_Space
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Homework Help Overview
The discussion revolves around understanding a specific subring of the complex numbers, defined as the set of ratios of polynomials where the denominator is not a member of the ideal generated by the polynomial x. Participants explore the implications of this definition and the characteristics of the elements within this subring.
Discussion Character
- Exploratory, Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants attempt to clarify the nature of the subring and question the implications of the restriction on the denominator. They discuss examples of elements that belong to the subring versus those that do not, and explore the significance of the ideal generated by x.
Discussion Status
The discussion is active, with participants providing examples and questioning the definitions involved. Some guidance has been offered regarding the characteristics of elements in and out of the subring, and there is an ongoing exploration of how to articulate these concepts clearly.
Contextual Notes
Participants note the importance of understanding the restrictions on the denominator and the implications of polynomials being multiples of x. There is also a focus on identifying elements that are not in the subring, particularly through the lens of polynomial characteristics.