MHB Proving Zp is a Vector Space for Prime p

[THEcj39]

How can I prove that
Zp is a vector space if and only if p is prime

 

[cbarker1]

What does the Z5 under addition and multiplication look like? What are the axioms of vector space?

 

[HOI]

A vector space over what field? Are you sure the problem is not to show that Zp is a field if and only if p prime?

 

[THEcj39]

A vector space over what field? Are you sure the problem is not to show that Zp is a field if and only if p prime?

The exercise doesn't specifies so I think is any field, and yes I'm sure the problem is vector spaces not fields

 

[HOI]

Any field is a vector space over itself so it is sufficient to show that Zp is a field if and only if p is prime.