Thread: quotient rings 6

If a^2=0 in R, show that ax+xa commutes with a.

Please show steps. Thanks!

Originally Posted by mpryal

If a^2=0 in R, show that ax+xa commutes with a.

Please show steps. Thanks!

do you know what "commutes" mean? you have to show that a(ax + xa) = (ax + xa)a

it is trivial to show that this is true. just compute each side separately. (do not assume that you have commutativity otherwise).