Let R be a ring What are the units of Rx JustifySolutionThe

Let R be a ring. What are the units of R[x]? Justify

Solution

The unit in R will be same as R[x]

f(x) is a unit in R[x], given a polynomial g(x) with the degree g(x) being d(g)

f(x)g(x) = 1

0 = d(1) = d(fg) >= d(f) + d(g)

Then both the things have f and g have zero degree, f0 is the unit in R[x]