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Ryan
Ryan, Engineer
Category: Calculus and Above
Satisfied Customers: 9016
Experience:  B.S. in Civil Engineering
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Use the definition for a ring to prove that Z7 is a ring under the operations + and × defined as follows:
[a]7 + [b]7 = [a + b]7 and [a]7 × [b]7 = [a × b]7
Submitted: 1 year ago.
Category: Calculus and Above
Customer: replied 1 year ago.
Sorry this is the entire question...
Use the definition for a ring to prove that Z7 is a ring under the operations + and × defined as follows:
[a]7 + [b]7 = [a + b]7 and [a]7 × [b]7 = [a × b]71. State each step of your proof.
2. Provide written justification for each step of your proof.B. Use the definition for an integral domain to prove that Z7 is an integral domain.
1. State each step of your proof.
2. Provide written justification for each step of your proof.
Expert:  Ryan replied 1 year ago.

Hi,

Thank you for using the site. I'll have the solution for this posted for you shortly.

Ryan

Expert:  Ryan replied 1 year ago.

Hi again,

Here are the solutions:

Ring

Thanks,

Ryan