Let S={[(0 r, 0 0)]| r is a real number} . Define a multiplication, * and an addition, α, on S under which S is a field.
Let's see some work? A field is a commutative skew field. Break that into three parts. Can you find a multiplication and addition such that it turns $\displaystyle S$ into A) a ring B) a ring which commutes under multiplication C) has multiplicative inverses.