Hi:
In a textbook I find: if A, B, C are right ideals in a ring R, then A(B+C) = AB+AC. This I have prove. But I could also prove (A+B)C = AC+BC (1)
where again A, B, C are right ideals in R. Can (1) be true? Any hint will be welcome.
Hi:
In a textbook I find: if A, B, C are right ideals in a ring R, then A(B+C) = AB+AC. This I have prove. But I could also prove (A+B)C = AC+BC (1)
where again A, B, C are right ideals in R. Can (1) be true? Any hint will be welcome.
yes it is true even for left ideals. since the product of (left, right or two-sided) ideals is defined to be we only need to prove that and for all these are very easy to prove: