Mathematics — Unit 1 — Test 20

Let R be a PID. Then every finitely generated torsion R‑module is

In Z[√−5], 6 factors as

In R[x], if a∈R is nilpotent (a^k=0), then for f(x)=x^n+a the polynomial is

Let R be a UFD. Which statement is true?

The nilradical √(0) of a commutative ring R equals

Over a field F, the polynomial x^p−a (p prime) is irreducible in F[x] if

In Z/nZ, an element [a] is a unit iff

If R is an integral domain and a,b∈R are nonzero zero‑divisors, then

If R is Noetherian, which is true?