prove the surjective of function [on hold]

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Let $R$ be the ring $F_2+ vF_2$, where $v^2= v$ and define $f: R rightarrow F_2^2$

Let $x= a + v b$ , where $v^2= v $ and $a$, $b$ elements $ in F_2 $



if $f(x) = f( a + v b) = ( a , a+ b )$ prove $f $ is onto.




linear-algebra abstract-algebra




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put on hold as unclear what you're asking by José Carlos Santos, Jyrki Lahtonen, TheGeekGreek, lulu, John Ma 2 days ago


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.














  • This is not clear. what is the domain of the function? What is its range? Also, when you edit your post for clarity please include your efforts on the problem.
    – lulu
    2 days ago










  • Try to give a more precise question. Where does $v$ come from, is $F_2$ the finite field of two elements? From where to where does $f$ map? But most importantly, what have you tried?
    – zzuussee
    2 days ago










  • Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    2 days ago






  • 1




    The elements of $F_2^2$ are $(0,0),(0,1),(1,0)$, and $(1,1)$. You only need to evaluate $f$ and see if it manages to spit out all those values: $f(0+v0)=(0,0)$, $f(1+v0)=(1,1)$, $f(0+v1)=(0,1)$, and $f(1+v1)=(1,1+1)=(1,0)$
    – spiralstotheleft
    2 days ago














up vote
-1
down vote

favorite












Let $R$ be the ring $F_2+ vF_2$, where $v^2= v$ and define $f: R rightarrow F_2^2$

Let $x= a + v b$ , where $v^2= v $ and $a$, $b$ elements $ in F_2 $



if $f(x) = f( a + v b) = ( a , a+ b )$ prove $f $ is onto.




linear-algebra abstract-algebra




share|cite|improve this question













put on hold as unclear what you're asking by José Carlos Santos, Jyrki Lahtonen, TheGeekGreek, lulu, John Ma 2 days ago


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.














  • This is not clear. what is the domain of the function? What is its range? Also, when you edit your post for clarity please include your efforts on the problem.
    – lulu
    2 days ago










  • Try to give a more precise question. Where does $v$ come from, is $F_2$ the finite field of two elements? From where to where does $f$ map? But most importantly, what have you tried?
    – zzuussee
    2 days ago










  • Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    2 days ago






  • 1




    The elements of $F_2^2$ are $(0,0),(0,1),(1,0)$, and $(1,1)$. You only need to evaluate $f$ and see if it manages to spit out all those values: $f(0+v0)=(0,0)$, $f(1+v0)=(1,1)$, $f(0+v1)=(0,1)$, and $f(1+v1)=(1,1+1)=(1,0)$
    – spiralstotheleft
    2 days ago












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











Let $R$ be the ring $F_2+ vF_2$, where $v^2= v$ and define $f: R rightarrow F_2^2$

Let $x= a + v b$ , where $v^2= v $ and $a$, $b$ elements $ in F_2 $



if $f(x) = f( a + v b) = ( a , a+ b )$ prove $f $ is onto.




linear-algebra abstract-algebra




share|cite|improve this question













Let $R$ be the ring $F_2+ vF_2$, where $v^2= v$ and define $f: R rightarrow F_2^2$

Let $x= a + v b$ , where $v^2= v $ and $a$, $b$ elements $ in F_2 $



if $f(x) = f( a + v b) = ( a , a+ b )$ prove $f $ is onto.





linear-algebra abstract-algebra





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited 2 days ago









Jyrki Lahtonen

104k12161355




104k12161355









asked 2 days ago









Alaa Yousof

22




22




put on hold as unclear what you're asking by José Carlos Santos, Jyrki Lahtonen, TheGeekGreek, lulu, John Ma 2 days ago


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.






put on hold as unclear what you're asking by José Carlos Santos, Jyrki Lahtonen, TheGeekGreek, lulu, John Ma 2 days ago


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.













  • This is not clear. what is the domain of the function? What is its range? Also, when you edit your post for clarity please include your efforts on the problem.
    – lulu
    2 days ago










  • Try to give a more precise question. Where does $v$ come from, is $F_2$ the finite field of two elements? From where to where does $f$ map? But most importantly, what have you tried?
    – zzuussee
    2 days ago










  • Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    2 days ago






  • 1




    The elements of $F_2^2$ are $(0,0),(0,1),(1,0)$, and $(1,1)$. You only need to evaluate $f$ and see if it manages to spit out all those values: $f(0+v0)=(0,0)$, $f(1+v0)=(1,1)$, $f(0+v1)=(0,1)$, and $f(1+v1)=(1,1+1)=(1,0)$
    – spiralstotheleft
    2 days ago
















  • This is not clear. what is the domain of the function? What is its range? Also, when you edit your post for clarity please include your efforts on the problem.
    – lulu
    2 days ago










  • Try to give a more precise question. Where does $v$ come from, is $F_2$ the finite field of two elements? From where to where does $f$ map? But most importantly, what have you tried?
    – zzuussee
    2 days ago










  • Welcome to MSE. Please read this text about how to ask a good question.
    – José Carlos Santos
    2 days ago






  • 1




    The elements of $F_2^2$ are $(0,0),(0,1),(1,0)$, and $(1,1)$. You only need to evaluate $f$ and see if it manages to spit out all those values: $f(0+v0)=(0,0)$, $f(1+v0)=(1,1)$, $f(0+v1)=(0,1)$, and $f(1+v1)=(1,1+1)=(1,0)$
    – spiralstotheleft
    2 days ago















This is not clear. what is the domain of the function? What is its range? Also, when you edit your post for clarity please include your efforts on the problem.
– lulu
2 days ago




This is not clear. what is the domain of the function? What is its range? Also, when you edit your post for clarity please include your efforts on the problem.
– lulu
2 days ago












Try to give a more precise question. Where does $v$ come from, is $F_2$ the finite field of two elements? From where to where does $f$ map? But most importantly, what have you tried?
– zzuussee
2 days ago




Try to give a more precise question. Where does $v$ come from, is $F_2$ the finite field of two elements? From where to where does $f$ map? But most importantly, what have you tried?
– zzuussee
2 days ago












Welcome to MSE. Please read this text about how to ask a good question.
– José Carlos Santos
2 days ago




Welcome to MSE. Please read this text about how to ask a good question.
– José Carlos Santos
2 days ago




1




1




The elements of $F_2^2$ are $(0,0),(0,1),(1,0)$, and $(1,1)$. You only need to evaluate $f$ and see if it manages to spit out all those values: $f(0+v0)=(0,0)$, $f(1+v0)=(1,1)$, $f(0+v1)=(0,1)$, and $f(1+v1)=(1,1+1)=(1,0)$
– spiralstotheleft
2 days ago




The elements of $F_2^2$ are $(0,0),(0,1),(1,0)$, and $(1,1)$. You only need to evaluate $f$ and see if it manages to spit out all those values: $f(0+v0)=(0,0)$, $f(1+v0)=(1,1)$, $f(0+v1)=(0,1)$, and $f(1+v1)=(1,1+1)=(1,0)$
– spiralstotheleft
2 days ago















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