For any R, any A belongs to D 1 intersection D2, because A belongs to D 1, so ra belongs to D 1, and A belongs to D2, so ra belongs to D 1 intersection D2. That is, D 1 intersection D2 is the ideal of R. ..

For any r, any d 1 belongs to D 1, and any D2 belongs to d2. Because D 1 and D2 are ideals of ring r, R 1 belongs to D 1.

Rd2 belongs to d2, so rd 1+rd2 belongs to D 1+D2, that is, r(d 1+d2) belongs to d 1+d2, that is, D 1+D2 is the ideal of R.

It's tiring to knock on math.