polinomis y espai vectorial quocient

E = s·(x^{2}+1)+i·(x+1)+j·1
F = k·(x^{2}+x+1)


s·(x^{2}+1)+i·(x+1)+j·1+(-k)·(x^{2}+x+1) € [E]_{F}


(p+1)k·(x^{2}+1)+(p+1)k·(x+1)+((-p)+(-1))k·1+(-k)·(x^{2}+x+1) = pk·(x^{2}+x+1)
(p+1)k·(x^{2}+1)+(p+1)k·(x+1)+((-p)+(-1))k·1 = [ pk·(x^{2}+x+1) ]+k·(x^{2}+x+1)
[ pk·(x^{2}+x+1) ]+k·(x^{2}+x+1) = (p+1)k·(x^{2}+x+1)


(m+1)k·(x^{2}+1)+(n+1)k·(x+1)+(q+(-1))k·1+(-k)·(x^{2}+x+1) = mk·(x^{2}+1)+nk·(x+1)+qk·1
(m+1)k·(x^{2}+1)+(n+1)k·(x+1)+(q+(-1))k·1 = [ mk·(x^{2}+1)+nk·(x+1)+qk·1 ]+k·(x^{2}+x+1)


dim(E/F) = dim( [E]_{F} )+dim(F) =4
[0]_{F} = pk·(x^{2}+x+1)
[u]_{F} = mk·(x^{2}+1)+nk·(x+1)+qk·1
F=[0]_{F}+F
E/F=[u]_{F}+F


E = s·x^{2}+i·(x+1)+j·1
F = k·(x^{2}+x+1)


s·x^{2}+i·(x+1)+j·1 + (-k)·(x^{2}+x+1) € [E]_{F}




(p+1)k·x^{2}+(p+1)k·(x+1)+0·1 + (-k)·(x^{2}+x+1) = pk·(x^{2}+x+1)
(p+1)k·x^{2}+(p+1)k·(x+1)+0·1= [ pk·(x^{2}+x+1) ]+k·(x^{2}+x+1)
[ pk·(x^{2}+x+1) ]+k·(x^{2}+x+1) = (p+1)k·(x^{2}+x+1)


(m+1)k·x^{2}+(n+1)k·(x+1)+q·1 + (-k)·(x^{2}+x+1) = mk·x^{2}+nk·(x+1)+q·1
(m+1)k·x^{2}+(n+1)k·(x+1)+q·1 = [ mk·x^{2}+nk·(x+1)+q·1 ]+k·(x^{2}+x+1)




dim(E/F)=dim( [E]_{F} )+dim(F)=4
[0]_{F} = pk·(x^{2}+x+1)
[u]_{F} = mk·x^{2}+nk·(x+1)+q·1
F=[0]_{F}+F
E/F=[u]_{F}+F