Math Help - Rings

1. Rings

Prove that in any ring R, 0 x a = 0 for all real numbers a.

Also prove that in any ring R,

(-1)a = -a for all real numbers a.

2. Originally Posted by meggnog
Prove that in any ring R, 0 x a = 0 for all real numbers a.

"For all REAL numbers..."?? What have real numbers to do here if R is a general ring? Read again CAREFULLY the axioms of ring theory and then use here that $a\cdot 0 = a(0+0)=$ ...

Also prove that in any ring R,

(-1)a = -a for all real numbers a.

The additive inverse of an element in a ring is UNIQUE , so prove (again, using the ring axioms, of course) that $(-1)a$ is an additive inverse of $a$ ...

Tonio

3. a is Natural, number or can be anything!?