Answer to Question #17191 in Algebra for Hym@n B@ss

Question #17191

Let R = Mn(D) where D is a division ring. Let S ⊆ R be a nonempty nil set which is closed under multiplication. Show that Sn = 0

Expert's answer

Download Answer

Learn more about our help with Assignments: Algebra Elementary Algebra

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. Show that a nonzero ring R is simple iff each simple left Rmodule is faithful
2. Show that N ⊆ M ⇒ μ(N) ≤ μ(M).
3. Show that μ is subadditive, in the sense that μ(M ⊕ N) ≤ μ(M) + μ(N) for finitely generated
4. Generalize the computation of μ(M) to the case of a finitely generated left module M over a semisim
5. For any finitely generated left module M over a ring R, let μ(M) denote the smallest number of elem
6. Let Ai(1 ≤ i ≤ n) be ideals in a ring R, and let A =(intersection) Ai. If each R/Ai is semisimpl
7. True or False: “If I is a minimal left ideal in a ring R, then Mn(I) is a minimal left ideal in Mn