Să se verifice dacă operatia algebrică , "" definită pe mulțimea [tex]M[/tex] admite element neutru:
a) [tex]\mathbf{M}=\mathbb{R}, \mathbf{x} \circ \mathbf{y}=\mathbf{2 x y}+\mathbf{x}+\mathbf{y}[/tex]
b) [tex]\mathbf{M}=\mathbb{C}, x \circ y=x y+2 x+2 y+2[/tex];
c) [tex]\mathbf{M}=\mathbb{Z}, \mathbf{x} \circ \mathbf{y}=\mathbf{x y}-\mathbf{3 x}-3 \mathbf{y}+12[/tex];
d) [tex]\mathbf{M}=(-\mathbf{1}, \mathbf{1}), \mathbf{x} \circ \mathbf{y}=\frac{\mathbf{x}+\mathbf{y}}{\mathbf{1}+\mathbf{x y}}[/tex];
e) [tex]\mathbf{M}=\boldsymbol{Z}_{7}, \mathbf{x} \circ \mathbf{y}=\mathbf{x y}+\hat{\mathbf{5}} \mathbf{x}+\hat{\mathbf{5}} \mathbf{y}+\hat{\mathbf{6}}[/tex]