Answer to Question #17358 in Abstract Algebra for sanches

Abstract Algebra

Question #17358

Compute the radical of the ring Tn(k) of n × n upper triangular matrices over any ring k.

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Related Questions

1. For a triangular ring T = R M 0 S (where M is an (R, S) - bimodule), show that rad(T) = rad(R) M 0
2. Show that, for any direct product of rings Ri, rad ((direct product)Ri) = (direct product) rad Ri.
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5. If an ideal I ⊆ R is such that R/I is J-semisimple, show that I ⊇ rad R.
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7. Show that rad R is the intersection of all modular maximal left (resp. right) ideals of R.