Let R be the set of all a in rational numbers in whose reduced form the denominator is not divisible by a fixed prime p. Verify R is a ring under the usual addition and multiplication in rational numbers. Find all invertible elements in R.
A component in a manufacturing process breaks down regulary and needs to be replaced by a new component. Assume that the lifetimes of components are i.i.d. random variables. The company adopts this policy: a component is replaced when it breaks down or after it has operated for time "a"...