Recent content by sarah77

Homework Statement Is U13 cyclic? The Attempt at a Solution I know the elements are {1,2,3,4,5,6,7,8,9,10,11,12}. I have eliminated 1,2,3,4,5 and I am working on 6. I am doing it this way: 60=1 61=6 62=10 63=8 64=9 65=2 ..and so on, but I did, for example, 62=36-13=23=10...

Ok, thank you so much!

Does anyone know how to find a generator for U13? I know the elements are {1,2,3,4,5,6,7,8,9,10,11,12}. I have eliminated 1,2,3,4,5 and I am working on 6. I am doing it this way: 60=1 61=6 62=10 63=8 64=9 65=2 ..and so on, but I did, for example, 62=36-13=23=10 and that is how...

ok, so the division was correct then? All of it? Thank you for checking my work!

It is in Z5, so I cannot use 2/3, it would be 3-1 and I tried that and it was incorrect..

It is in Z5 so 3x4=12 which is 2 in Z5 or am I missing something? I cannot use fractions, I don't think 2/3 is in Z5

Has anyone been able to read my work and critique it? Please let me know if I am on the right track..

Homework Statement Is U(13) cyclic? Is U(15) cyclic? 2. The attempt at a solution The units in U(13): {1,2,3,4,5,6,7,8,9,10,11,12} U(13) is not cyclic because it is prime? U15:{1,2,4,7,8,11,13,14} and there are no generators either? I do not think I am correct with this though.

I have attached my work to this reply. Is this correct?

I have attached the work I have done so far, please critique and help me finish. I am confused on what -3^-1x^3 becomes in Z5. Does it become 3x^3?

Homework Statement Divide 2x5+x-1 by 3x2+1 in Q[x], Z5[x], and R[x] The Attempt at a Solution I believe the answer should be the same in Q[x] and R[x] and after division I got 2/3x3-2/9x with remainder 1 2/9x-1. I had trouble in Z5 and would like someone to help me. So far I...

I know there are several properties that must be met in order for the set to be a ring: associative under addition and multiplication; commutative under addition; and distributive. How do I begin checking these properties the set of all pure imaginary complex numbers?

Homework Statement Determine whether the indicated operations of addition and multiplication are defined (closed) on the set, and give a ring structure. If a ring is formed, state whether the ring is commutative, whether it has unity, and whether it is a field: The set of all pure...

The Unit in 2Z is 1, so the multiplicative identity element in 2Z x Z is 1; does that mean that all numbers are units in 2Z x Z?

Homework Statement Describe all the units (if any) in each given ring: 2Z X Z with addition and multiplication by components; and Z X Q X Z with addition and multiplication by components Homework Equations The Attempt at a Solution I do not know how to begin, I am not sure how...