Unformatted text preview: it has nontrivial right ideals.) (b) Let R be the ring of 2 × 2 matrices over the reals and suppose that I is an ideal of R . Show that I = (0) or I = R . 5. Let R = Z [ i ], the ring of Gaussian integers . Starting with R , construct a ﬁeld having 49 elements. 6. Find all the units (invertible elements) in the ring Z 24 7. Let R be a ring in which x 4 = x for every x ∈ R . Prove that R is commutative. 8. If a,b ∈ Z such that either 3 6 | a or 3 6 | b (or both) show that 3 6 | ( a 2 + b 2 )...
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- Spring '11
- Algebra, finite integral domain, nontrivial right ideals, nontrivial left ideals