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Vector space

THEcj39

New member
Nov 14, 2020
2
How can I prove that
Zp is a vector space if and only if p is prime
 

Cbarker1

Active member
Jan 8, 2013
242
What does the Z5 under addition and multiplication look like? What are the axioms of vector space?
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
537
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

New member
Nov 14, 2020
2
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
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
537
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.