can someone check my labels for the reaction of a radical with an extra electron, (R(e-)) and an antioxidant, ArOH.

R(e-) + ArOh --> RH + ArO(e-)

R(e-) is oxidizing agent.
ArOH is reducing agent.
RH is reduced
ArO(e-) is oxidized.

Is this correct?

And the other possible reaction,

R(e-) + ArOH --> R- + ArOH(e-)+

R(e-) is reducing agent.
ArOH is oxidizing agent
R- is oxidized
ArOH(e-) is reduced. ?

I don't understand the post. For example is R(e-) and R^- the same?

R(e-) is having the extra electron and R- is the anion i think

Yes, your labels for the reaction with a radical (R(e-)) and an antioxidant (ArOH) are correct.

In the first reaction, R(e-) is the oxidizing agent because it accepts the extra electron and gets reduced to RH. ArOH is the reducing agent because it donates the electron to R(e-) and gets oxidized to ArO(e-).

In the second reaction, R(e-) is the reducing agent because it donates the electron to ArOH and gets oxidized to R-. ArOH is the oxidizing agent because it accepts the electron from R(e-) and gets reduced to ArOH(e-).