Proving the identity of the field

In summary, the conversation discusses the verification of the field axioms for a given abelian group, with a focus on the existence of the identity for the multiplicative operation. The group is defined as S = {s in R such that s=/=1} and the operation is a*b = a + b - ab for a, b in R. The identity is identified as 0, and it is discussed how it satisfies the given condition for all a in R.
  • #1
playa007
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0

Homework Statement


If S = {s in R such that s=/=1} is an abelian group under circle operation (Circle Operation a*b = a + b -ab for a, b in R) then R is a field

Homework Equations


The verification of the field axioms

The Attempt at a Solution


The field axiom that I'm struggling to verify is the existence of the identity for the multiplicative operation since s=/=1. I'm wondering if someone can help me resolve this.

Thanks
 
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  • #2
Isn't the identity 0? Why do you think it's not?
 
  • #3
If aob= a+ b- ab Then the identity, e, must satisfy a+ e+ ae= a for all a. Solve that for e.
 

What is the importance of proving the identity of a field?

Proving the identity of a field is crucial in scientific research as it helps to establish the validity and reliability of the data collected. It ensures that the data represents the intended phenomenon and can be used to draw accurate conclusions.

How is the identity of a field determined?

The identity of a field is determined through rigorous experimentation and data analysis. This involves conducting controlled experiments, collecting and analyzing data, and comparing the results to established theories and principles.

What methods are used to prove the identity of a field?

Scientists use a variety of methods to prove the identity of a field, including statistical analysis, peer review, replication of experiments, and the use of multiple data sources. These methods help to verify the consistency and accuracy of the data collected.

What are the potential challenges in proving the identity of a field?

One of the main challenges in proving the identity of a field is the presence of confounding variables that may affect the results. It is also important to consider the limitations of the methods used and potential biases in data collection and analysis.

How can the identity of a field be validated?

The identity of a field can be validated through the acceptance and recognition of the findings by the scientific community. This involves publishing the results in reputable journals, presenting them at conferences, and engaging in discussions and debates with other scientists in the field.

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