Mathematics — Unit 1 — Test 21

Let R be a ring and M a finitely generated R‑module. If R is Artinian, then

In Z[x], the content c(fg) equals

Let k be a field. The ideal (x,y) in k[x,y] is

If R is a PID and a|bc with gcd(a,b)=1, then

Over a field F, the ideal (x^2+1) in F[x] is maximal iff

In Z, the number of solutions to x^2≡1 (mod 2^k) for k≥3 is

A finite field has order

The multiplicative group of a finite field F_q is

Over F_p, the polynomial x^{p^n}−x