Recent content by frnkarich

By criterion theorem, S is a subring of R iff x-y E R and xy E R for all x, y E S so you must show these two are true. So let x,y E Z(R) and r E R, To show x-y E Z(R), you have to look at r(x-y). by definition, rx=xr and ry=yr, so r(x-y)= rx-ry = xr-yr= (x-y)r so x-yE Z(R). (This...